Do not invite home-video exercise queens Jane Fonda and Callan Pinckney to the same health club. They just might wind up throwing dumbbells at each other.

These bitter rivals - each hawking a different approach to exercising - have never met. They just snipe at each other in print. Their feud, which had been recognized only in home-video circles until recently, has gone public now that both have been promoting new tapes.Fonda's latest - "Jane Fonda's Complete Workout" (Warner, $29.98), her 10th - was released two weeks ago. Pinckney's "Supercallanetics" (MCA, $24.95) came out last fall, a follow-up to "Callanetics," a 1986 release that has grabbed a share of the market that has been totally dominated by Fonda.

Referring to her new tape, Fonda, a youthful-looking 51, said: "It's scientific, it's fun, it's safe, it works, it's the best tape out there."

In a separate interview, Pinckney, a youthful-looking 50, said: "Callanetics are safe, they're fun, they work incredibly. My tapes are the best ones on the market."

Chiding Callanetics, Fonda said: "If I did (in my tapes) what she did, I'd be shot out of the water - from a medical and safety point of view."

About Fonda's tapes, which feature aerobics, Pinckney said: "People are hurting themselves with aerobics. There's too much stress on the joints and on various parts of the body. That kind of exercising does more harm than good."

Commenting on the feud, one home-video executive insisted: "They're just jealous of each other. Jane doesn't like anybody butting in on her turf. She created the whole market. And Callan resents Jane's success. But `Callanetics' is getting bigger all the time. If `Callanetics' wasn't around, some of those buyers might have bought Fonda tapes."

Though there are hundreds of exercise tapes on the market, only Pinckney has been a real challenge to Fonda (Media Home Video's Kathy Smith is a distant third). In two years, Pinckney's "Callanetics" has sold 703,000 copies, according to Video Marketing Newsletter, referring to sales to retailers and distributors. That placed her 32nd on the newsletter's list of the 100 top sellers of all time.

But Fonda has four tapes higher on the list.

Three Fonda tapes are in the Top 20 and four in the Top 30. Two - "New Workout" (1985) and "Low Impact" (1986) - sold more than 1 million copies. Sales of her first tape, "Jane Fonda's Workout," are at 950,000. A short tape, "Start Up With Jane Fonda" - sold 780,000, and her "Prime Time Workout" has sold more than 500,000.

Each of the women champions an exercise style that conflicts with what the other is promoting. The tapes are equally dissimilar.

Aerobic exercises - done to a disco beat - are the centerpiece of Fonda's approach, which she has expanded to include dumbbell work. It's all flashy, high-energy and fairly high intensity. Fonda's tapes have a glitzy, show-biz sheen.

Pinckney's Callanetics are low-intensity muscle contractions and stretches largely based on ballet movements. Like her exercise style, her videos are low-key. There is neither glitz nor loud music. The exercises are delicate, tiny movements.

Comparing her exercises to aerobics, Pinckney said, "Aerobics are intimidating. It looks like you have to be young and athletic and already in good shape just to do them. My exercises aren't intimidating. They're lots of small, precise movements. But they work deeply on the muscles to tighten droopy stomachs and behinds. Callanetics attack the saddlebags and droopy behinds that women get as they get older. One hour of Callanetics equals many hours of aerobics."

But she hasn't convinced Fonda, who charged, "My exercises are safer. You can change your body to some extent using Callanetics, which is the kind of exercise where you repeat a movement and use a muscle group over and over. But it's not enough. You need that aerobic component."

Pickney notes with glee, however, that many exercise physiologists now recommend less rigorous aerobic exercises.

"High-intensity aerobics aren't good for everyone," Fonda acknowledged. "It's better to work out less intensely for a longer period of time. Now I do aerobics in a way that enables people who don't like to do a lot of jumping around to do aerobics."

Those principles were incorporated in her 1986 "Low-Impact" tape. Her new tape is even more advanced, featuring both high-intensity (for advanced students) and low-impact aerobics, as well as exercises with weights.

Who's right?

"People have to make that decision for themselves," one home-video executive concluded. "There's good in both programs. As long as people are exercising - doing something - that's the important thing."