TIL that trees are the same as vegetables and weeds, arbitrary cultural groupings. We should make an arbitrary cultural group name for arbitrary cultural grouped things!
So far the group is:
-Trees
-Vegetables
-Weeds
-Pets
-Continents
-The culinary use of fruit
Nope, that's not how the definition of a tree works. Look at swednek's definition in the comments: it is a woody trunk with branches. There are many other plants you could make toothpicks out of (e.g. that are woody) that aren't trees. For example, shrubs and lianas.