I would recommend to make "cart" and "classification-tree" tags junior synonyms of "decision-tree". Because, often CART acronym is regarded to be just a particular method or algorithm of the tree building, along with other methods such as CHAID or QUEST. Decision Tree seems currently to be the most omnibus term.
Some relevant facts:
- We seem to have four tags related to this discussion: cart, decision-trees, tree, & classification-tree.
- At present, decision-trees & tree are synonyms that automatically map to cart. On the other hand, classification-tree is distinct, but indexes only two threads, one of which is also categorized under cart.
- It's also worth recognizing that making a tag a synonym makes it much more difficult to find questions categorized under the old tag, and this problem has not been resolved.
The points you raise are good ones, but I agree with @whuber that it might not be best to change the current pattern of synonyms. My suggestion would be to edit cart's tag wiki excerpt to indicate more accurately how it ought to be viewed / used by the community. There is a linguistic phenomenon in English (and probably all languages) whereby the name of a particularly salient member of a category comes to stand for the category as a whole. (For example, Kleenex is a proprietary / brand name, but is used to indicate any facial tissue.) I can imagine "cart" coming to be used (perhaps incorrectly) the same way.
Because a decision tree is a generic method that goes well beyond CART or classification, I would be reluctant to make it a synonym.