Slim Fit jeans have the least fabric in the rear panels, and the thigh openings are narrower than the regular fit. They’re designed to hug your body. These are good for guys with tight butts who want to show their figure off, and uncomfortable and unsightly on most everyone else.
Regular Fit jeans are what most of us wear. The exact measurement varies a bit from brand to brand, but they’re made to fit like traditional blue jeans: resting lightly against the buttocks in the back, with a bit of wiggle room in the crotch. Unless you’re packing some extra weight in the butt or thighs, this is probably the fit you want.
Relaxed Fit adds fabric in the back and extends the rise a little, as well as expanding the leg openings. We tend to associate them with overweight men, but they’re just as useful for men with “footballer butt” — strong glutes and thighs paired with narrower waists and calves. A lot of athletes end up needing relaxed-fit jeans.
Understand that these aren’t very scientific terms. Each brand has their own in-house stylists, with their own idea of what a “normal” person’s butt and thighs look like.