Drew, honeysuckle strangles trees as it twines around their trunks resulting in the contorted corkscrew growth. Wild grapes usually just drape over other plants with only tennicles twining to attach them. Other vines like bittersweet may also contort tree growth like in the pics but from what I've seen it is mostly honeysuckle that causes these corkscrew trees.
The common honeysuckle I'm referring to is Lonicera japonica(Japaneese honeysuckle, an invasive exotic that was planted by the wildlife folks for food and cover for animals.