Vines are not a special group of plants, but - like trees and shrubs - defined by appearances. Vines have long stalks/shots/branches that are too weak to support themselves. Usually vines are divided in two subgroups, creepers and climbers:
Creepers are vines that - if left alone - trail over the ground or hang down. If gardeners want them to grow upwards, they must tie them to some supporting structure. Creepers are often used as ground cover.
Climbers on the other hand, are vines that can climb on their own. They either
- wrap their entire branch around supporting structures (like wisteria),
- grow tendrils (sweat peas) or tendril-like leaves (clematis) or
- have some sort of special aerial rootlets (English ivy) or adhesive pads (Virginia creeper -> a misnomer!)
If no supporting structure is available, climbers will "creep" over the ground, too, of course.
Caveat: The naming is not always consistent, "Virginia creeper" is actually a "climber".
Edit as requested:
There is another type of "creepers", namely ground-covering or "crouching" plants without long "vine-like" branches. Creeping thyme is an example.
As all names in this post are based on apperance and not on some kind of botanical relationship, this was to be expected.