When Harold Solomon beat Arthur Ashe last week in the Italian Open Tennis championships at Rome, the most evident difference was not in their ability to stroke the ball, but in their movement on the slow red clay that is the surface of major competition on the continent.

Ashe never has been comfortable "on the dirt," as players who grew up on faster, firmer surfaces call clay - especially the dusty European variety that quickly turns their tennis shoes and socks the color of Mercurochrome.

Even though heavily watered European clay afford better footing than the more slippery, grittopped composition surfaces that pass for "clay" in the United States - such as the grayish Har-Tru courts on which the Washington Star International is played - Ashe never has felt at home on it. He has likened playing on it to "running on marbles."

It is uncertain footwork more than any technical deficiences in his ground strokes that makes Ashe, like so many other serve-volley-oriented. Americans and Australians, plead "nolo contendere" in the long baseline rallies that are an essential part of tennis on clay.

"I make mistakes on this stuff that I wouldn't on a court just as slow, but with firm footing," Ashe acknowledged. "That, plus indecision when I have the opportunity to hit an approach shot, are my biggest problems on "clay."

This was apparent in his 6-4, 3-6, 6-0 loss to Solomon in the third round at Rome.

Solomn, on the other hand, appears as if he would be content to gravel in the gravel forever.

He learned to play on a cement court in his backyard in Silver Spring, Md. It is a myth that he grew up hitting topskin loopers on clay the way Eddie Dibbs did, stroking moonballs over Miami - But he moves well on "dirt," sliding into shots almost as naturally Eurfopeans for whom it is the native soil.

"Harold is good at sliding and then recovering. He moves easily from side to side. Arthur is accustomed to running to the ball and then pushing off, which is what you do on a firmer surface," said former U.S. Davis Cup Captain Dennis Ralston, a contemporary of Ashe who now coaches Solomon and five other American pros.

"Arthur moves forward much better than he does laterally. He runs a lot better than Harold does on grass. He is lighter on his feet and has a high center of gravity. Harold is built closer to the ground and he runs with a heavier stride, which helps him on clay.

"You've also got to remember that Harold has grown up with a lot more clay-court experience," added Ralston, noting that Ashe, 34, is part of a generation of American players that seldom completed in Europe and got their education when most American tournaments of consequence were played on grass or cement. Solomon, 25, is a product of the clay era.

Ashe came to Europe five days before the Italian open and worked out eight hours a day with Ralston, Solomon, Brian Mottfried, Roscoe Tanner and Bjorn Borg at Monte Carlo. But he had realistic expectations of what he could do in Rome and now in Paris - where he faces a tough match today against Australian Phil Dent, a semifinalist last year, in the first round of the French Open, the world's premier claycourt test.

"I don't have any illusions about winning the French. I'll be fortunate to last to the second week, but I do think I can play better on the clay than most people think I can, especially when I've had time to get acclimated," Ashe said.

"In any event, now that there are two weeks of tournaments on grass between Paris and Wimbledon, the European tournaments are great training grounds. Long, tough matches on clay are terrific for stamina and condition."

Solomon, who was wiped out by eventual champion Borg in the quarterfinals at Rome, has more immediate concerns. "This is the biggest tournament of the first half of the year for me. The French is my Wimbledon," he said.

He was runner-up here in 1976, beating Guillermo Vilas in the quarters and Raul Ramirez in the semis before losing a rugged four-setter to Adriano Panatta in the final. If the seedings hold up, Solomon will again meet Vilas, now the defending champion, in the quarters this year.

The 5-foot-6, 138-pound Solomon does not have the serve or volley to do well on grass, a surfact on which his record is miserable. Last year he lost in the first round at Wimbledon to a rather anonymous big server named Steve Docherty. This year he did not file an entry for Wimbledon.

SOlomon was not playing well going into Rome. He was thrashed by Spaniard Jose Higueras in the Nations Cup at Dusseldorf, West Germany, and by Chilean Belus Prajoux in the first round of a tournament in Florence, Italy.

Though he has not had a particularly distinguished first five months of 1978, Solomon did win the $50,000 first prize in the Alan King Classic at Las Vegas a month ago and says he is reasonably satisfied.