You would not say "on the tree" unless you were talking about something that is actually part of the tree (like leaves). For example: "Look at the leaves on the tree!" Otherwise, you should say "in the tree" (like when talking about a person or animal). "She is sitting in the tree." "There are birds in the tree." I disagree slightly with the other person who answered. "In the tree" doesn't really suggest hiding, it's just the way you would say that sentence. You should use "in the tree" even if a bird is at the top of the tree (at least that is how it is said here in America). I rarely here people say "there is a bird on the tree."

Both of them suggest more or less the same thing, being physically on the branches of the tree, but vary slightly in the position in which the subject is found. "In the tree" suggests a sense of hiding. 'The bird is hiding in the tree, safe from its predators'. "On the tree" often refers to something that is sitting on the highest point of the tree and is more often used when we are looking above the trees. However, it can also have the same meaning as being within the trees. So maybe when you are walking in a nature trail, you can indicate to your friend, "Look! There is an owl ON the tree." Hope that helps!