A naturalistic tree is not to be confused with one that is realistic, which is as close to real life as possible. A naturalistic tree is designed to have real-life attributes but is obviously not as real-looking as it could be. It is not as detailed as a realistic tree. A naturalistic tree should be size appropriate. Limbs should be proportionate to the trunk and leaves, if there are any. This tattoo would need a decent amount of room for detail.
An idealistic tree is an "ideal" tree. It would be similar to that of a cartoon, with a big, fluffy green top and a brown trunk, maybe with a knot in the middle. Trees that are idealistic have vivid colors and a perfect shape. This tree would be nicely shown in any size, and would go well with other idealistic objects, like a rainbow, pot of gold or a bird.
A distorted tree still resembles a tree, but in its distorted form. Over-extended branches, over-size leaves or a lengthened and wavy trunk would be characteristics of a distorted tree. For a tattoo, it would be best to use a good amount of room and make it as large as possible so that it remains distinct. In a smaller size, the tattoo may not look like a tree at all.
An abstract tree is similar to tribal art. The tree, although visually similar in shape to any tree, would be created in parts or blocks. This tree can stand alone in a tattoo, but should be at least medium-size for detail. An abstract tree can be completely unique.