Though “clinging” and “vine” seem like a wedded concept, only a few vines really do hold on that way, using aerial rootlets that act as suction cups to attach themselves to their support. These rootlets are very strong and enable even very heavy vines to rise high on flat walls. Examples include climbing hydrangea, Boston ivy, and English ivy.
More commonly, vines are inclined to twine, wrapping their main stems around the nearest available support and circling it as they grow. Examples include beans, morning glories, bougainvillea, hops, hoya, and wisteria.
The other large group are tendril-climbers, which send out specialized, leafless stems
that wrap tightly around any adjacent object that’s thin enough to get a grip on. Examples include peas, cup-and-saucer vine, grapes, passionflower, and porcelain vine. The specialized stems that do the holding on can also have leaves, in which case they’re called petioles. Clematis are the best known petiole users, but Climbing Snapdragons (asarinas) also climb this way, and so do those rare nasturtiums that genuinely climb.
But not all vines do genuinely climb. Some just head for something supportive and grow on, around, over, or through it, sending out a tendril or two, applying a rootlet, or twining a bit without behaving in and recognizably organized way. Expect to receive some guidance if you plant these and have a particular direction of growth in mind. Examples include trumpet vine, silver-lace vine, and some of the jasmines.