TWO DIFFERENT sets of questions have become central in the Democratic and Republican contests for president. The dominant questions concerning the Democratic candidates are: what do they know and what do they think? Those concerning the Republicans are: what are they like and how are they likely to behave? Opinion vs. personality, ideas vs. fundamental nature. The distinction isn't absolute, of course. On the Republican side there is much heaving and ho-ing about who might -- perish the thought -- acquiesce in or even seek a tax increase, while on the Democratic side there are charges of duplicity and flip-flop and there is also the continuing saga of Gary Hart. But that is the basic split: George Bush and Bob Dole especially are trying to show that each of their (utterly different) temperaments and styles of doing things are, contrary to some misgivings, suitable and safe for the presidency, while the Democrats are trying to prove -- also contrary to some misgivings -- that their ideas are not half-baked or grounded in ignorance or pandering.

Mr. Bush had a good night in New Hampshire. He beat Mr. Dole and all the other candidates comfortably, and if he didn't finish with the 20-point lead he had once enjoyed in the polls, he did manage to arrest an alarming post-Iowa proc-ess of political evaporation that at one point had seemed to threaten his prospects altogether. But the vice president still seems uncomfortable and off-pitch in his attempts to remedy the defects in his public persona that practically everyone, including notably his public relations advisers, has identified as a major problem. When Mr. Bush tries to go "tough guy" in his prose and stance -- barroom and/or barnyard -- it sounds awful. Probably he should accept it as a fact and conceivably even a virtue that he makes a wholly implausible Stanley Kowalski. He should probably also abandon efforts to explain the hardships of growing up privileged, which can scarcely be expected to elicit much sympathy from anyone else.

But unsettled and uncommanding as Mr. Bush's projected personality may still be, he did receive some help from Mr. Dole, who, both before and after the results were in, lapsed back into a kind of nasty wise-guy style that must surely turn off and perhaps even frighten as many people as it entertains. These two men talk a lot about leadership and being presidential and the rest. Never mind that it is almost a condition of being presidential that one does not talk about how marvelously presidential one is. Republican voters (and independents attracted to the Republican Party) must know that there is not much of a gulf between them on the issues, that the "who is more presidential?" question is the main one. Mr. Bush has to fight the drag of the vice presidency, Mr. Dole the charge -- and perception -- that upbringing strictly as a legislator does not really equip a person for executive office. More importantly, it seems to us, both have to establish their particular personal fitness for the job. That is what their fight is about, and it is just getting started.

For the Democrats it is the other way around. The personalities, excepting a couple of them, seem surpassingly bland -- worked out, unexceptional, arranged. It is what they are saying that generates the conflict and doubt. For example, Gov. Dukakis, who won an impressive victory in New Hampshire, was at pains there to try to toughen up his foreign policy positions. How deeply are his convictions on the subject held? How knowledgeable is he on all this? A New Hampshire editor said his paper, interviewing Mr. Dukakis, found his foreign policy views generally "book-learned." But the Massachusetts governor nonetheless gets pretty categorical and even self-certain in his pronouncements in this field. More than people in the South (to whom, it is said, his slightly revised positions are meant to appeal) will be trying to measure his competence, authority and insight in this whole area as the primaries go on. Sen. Gore, who has himself been accused of simulating a rightward position on national security affairs, to distinguish himself from the pack, will no doubt make this a large issue between them.

Rep. Gephardt's views are the other large question. He emphatically denies that they keep changing or that he has been pandering to and fueling grievances that he knows a president cannot responsibly assuage by the means he now endorses. Having risen in the House as an accommodative sort, he now turns out to have a demagogic streak. It seems to have paid off in both early contests, where he revived and prospered. He has become a proud tax-cutter at a time when it is plain that a Democratic president to fulfill his commitments will almost certainly have to try to raise taxes.

The Democrats were going to "rethink" their positions eight years ago, so as to be modern, ready and relevant when their next real presidential opportunity came. It is here. People are still trying to figure out where that rethinking, if it took place at all, has led them, just as they are trying to figure out whether a Bob Dole or a George Bush would be better suited by temperament, training and instinct to run the country.