LAWRENCE K. GROSSMAN is the president of the Public Broadcasting Service (PBS). This is not to be (confused with the Corporation for Public Broadcasting (CPB). In fact, however, it is confused with it all the time.

"My mother still doesn't know which I work for, CPB or PBS, or what the difference is," says Grossman at a conference table in his L'Enfant Plaza office. "All she cares about is when she turns on the damn set and sees what's coming out. And what's coming out on public TV is uneven, but it also often awfully terrific and very exciting."

The new public television season begins today, and Grossman sees it not as the moon, not as the stars, but as another step toward the ideal that for 25 years public television has managed to avoid. Among his reasons for hope are a communications satellite, newly installed in space, which enables PBS to transmit, at a relatively cheap cost, three different programs to its stations at one time.

But Grossman is also encouraged by the fact that Henry Loomis, a holdover from public TV's Cold War of the early '70s, has left his post as president of CPB - the PBS overlord - and been replaced by Robben W. Fleming, while Newton N. Minow has taken over as PBS chairman. What this means is that the final traces of the Nixon administration and its attitude of containment toward public TV are gone, and that the era of constant territorial bickering between CPB and PBS may be ending.

"Where Loomis has been coming from and where CPB has been coming from, and what really began in the Nixon years, is a totally local system for public TV," Grossman says. "That's what Loomis said; there should be no national programming, it should all be local, and every once in a while when something interesting comes up that has national interest, you could fund it.

"Now where we are coming from, where I come from and where this system comes from, is that it's very important that stations have their local stuff and their identity and provide a service to their own community. But television is also something else. It's the one national unifying element that we have, and the way to really strengthen your local stuff is to have compelling major programs to draw an audience, to serve as a centerpiece, and then to build on that."

There are a number of compelling major programs on the new PBS schedule. These include a seven-week festival of Eugene O'Neill plays: a new Sunday night series of original or acquired documentaries to include the controversial "California Reich"; a "Cinema Showcase" of 10 recent theatrical features that range from Lina Wertmuller's "Seven Beauties" and "Swept Away" to the muscleman saga "Pumping Iron"; Laurence Olivier, Alan Bates and Malcolm McDowell in Harold Pinter's enigmatic drama "The Collection" and early next year, the first six entries in an ambitious six year BBC and Time-Life project that will see new TV productions of all TV plays credited to William Shakespeare.

In addition, Grossman hopes to air much more live programming, including musical performances like the recent pop and classical concerts from Wolf Trap and the White House. "We have very substantially increased our efforts and energies and time devoted to live television which, to me, is really when television is at its most important and exciting," Grossman says. "We're up 43 percent in the next couple of months, over last year, in the amount of our live last year, in the amount of our live programming, and that's very significant."

Grossman wants to broaden the public TV audience and attract more young viewers. It will be easier said than done.

"We tend to have an older audience show," he says, in TV-talk. Once considered, with some justification, unrealistic and elitist in its program offerings and target audience - aiming much more eagerly at "Upstairs" than "Downstairs" - public TV is undergoing "a tremendous broadening of its demographics," Grossman says, with a recent survey indicating "the audience in nonwhite homes is up 42 percent" as the result of "a conscious effort" to attract minority group viewers. Grossman also claims that "the visibility of public television has increased phenomenally in the last two years.

The fact that PBS will be beaming programs to its stations by satellite - instead of over the standard telephone lines - will not make them look any different to home viewers or necessarily improve their quality. What it will do is give PBS stations greater flexibility in programming. They may be able to choose from a live senate hearing a taped concert or an instructional symposium putting one on the air and serving the others on tape. PBS is not a network, and it has no real power to force stations to show certain programs at certain times.

Grossman says he dosen't even want that power that it is the nature of public television to allow its stations a freedom of choice.

"I'm not one of those who thinks the satellite is going to save the world, either," he notes. "We've all had too much experience with the glorious new telephone, and radio, and television, and how they were going to bring peace and understanding, and how as soon as we could talk to each other across continents, there would be no more wars. In the end, it's the content that counts, and it's the only thing that counts, and how you get it to people doesn't make the slightest bit of difference."

One of the uses Grossman foresees for the satellite is in revitalizing public TV's daytime schedule, now dominated almost entirely by children's programs. Many stations with school-board subsidies and contracts will want to continue these, he says, but others in larger markets will be able to carry alternative adult programming. Grossman is especially anxious to cover more Capitol Hill hearings live, though when he pre-empted "Sesame Street" for hearings on President Carter's cabinet choices, "The stations almost handed me my head." The satellite will enable him to keep his head and his hearings.

For all the encouraging words about the evolution of public television, Grossman has to concede it is still wracked with awesome woes. The relationships between PBS and its stations are mercurial and tentative; larger production centers, like WGBH in Boston and WNET in New York, think it in their best interests to keep PBS weak, not strong and dynamic. The system is strangling on red tape and beset with bureaucratic boondoggles that are amazing, considering its relative youth; Grossman confesses to a "mess in our organization" and a sluggish lack of responsiveness in the system.

Ask anyone who has tried to get one program on the public air, it's a matter of rounding one corner after another in a labyrinth that would have impressed Kafka.

"It is an agonizing process, there's no question about that," Grossman says. "But the agony comes from several things. More than the bureaucracy is the money problem. We're just organized in such a way that we don't have gobs of money sitting around to put up for a program. If you have a program idea, you have to go to CPB and get a third of the funding, and go to a foundation to get a third of it, and to an underwriter if you can find one, or to the stations, and by the time you get it all together, it can drive you absolutely crazy. If we were decently funded, we wouldn't have that problem as much."

Of course the plea "more money" is practically a doorbell at public television. Unfortunately, public TV has a poor record when it comes to accounting for the money it does spend. Productions, especially the big tub-thumpers, are infamous for their excessive costs.

"Sure, that's a problem that we are aware of," says Grossman. "It's a self-fulfilling cycle, however. Take The Adams Chronicles' - a classy example, right? Just went bananas with the budget. But the interesting thing is, if you look at those budgets - which I did, because we're subject to attack - you see that, sure, the first half dozen episodes just went haywire - just as 'Battlestar Galactica' went through the ceiling at Universal - but then, just as the people were getting good at it, the last episodes came in not only on budget but under budget. It's like starting anything you haven't done before.

"Unfortunately, the money ran out, there was no project to be picked up, so that crew that had begun to work together, the people who learned how to do this stuff well, had to break up and start all over again. It goes back to the way we have to operate, which is, you have to stop, spend a couple years gathering enough money to put on a series like that, make the series, and then the people disband. In Boston they are having terrible production problems right now with 'The Scarlet Letter.' They'll get into the swing - and as soon as they do, the series is finished."

Grossman thinks there are solutions to all these problems. Indeed, it sometimes seems public TV inundates itself with solutions, or at least reports. In midsummer, PBS vice chairman Hartford N. Gunn Jr. submitted "a major report suggesting a complete reorganization of public broadcasting's structure." The Carnegie Commission, whose first report made recommendations for public TV funding still not enacted, is now preparing a second report which is expected to make some of the same recommendations. Reform of the public TV bureaucracy and improvements in funding are part of the current House rewrite of the Communications Act of 1934.

PBS is working on a report on itself and Grossman hopes that in June he can hold "a kind of constitutional convention of public broadcasting" which would put all the recommendations and reports together and "finally get this thing turned into what it is gradually becoming which is a very significant and major force in society. Which, as you know, is long overdue."

At least the White House isn't hostile any more, in fact, some say the Carter administration is too chummy with public television and is using it to enhance its own public image. Grossman does not see this as an imminent danger and doesn't want to turn down a chance to televise a recital by Leontyne Price - as PBS will on Oct. 8 - just because she happens to be singing from the White House and the First Family is in view.

Grossman, once an executive at NBC, seems a healthy combination of realist and visionary. He does tend to measure public television's success by the standards of commerical television - size of audiences for instance, and number of "specials" aired - but his kind of practical vigor is definitely needed in public broadcasting. One finds it heavily populated with the lethargic, the defeatist and the just plain dull. Grossman isn't too shy to boast about his victories, either.

"Not so long ago, inside of one week, we had Robert MacNeil and Bill Moyers stay with or come back to public television, instead of succumbing to the blandishments of the big fat folks (the commercial networks) up there," he says.

"Well, two years ago, that would just simply have been unheard of. I mean, a nibble from CBS, NBC, ABC and zoom, they were off."

However, Moyers is already saying from WNET in New York that he feels constrained by the tiny budgets being allotted for his public affairs reports. "He came in on faith," says Grossman, "and now we're all scrapping like crazy to get the money for him to do a series." He sighs a sigh sighed often in corridors of public television. "Money," he says. "Terrible problem. Terrible problem."