it sounds like that is everything included. I don't like the term "trim" because its vague but if you had crown moulding I'd expect that to be included aswell. Inside closets and the casing should be included and painted white so they never need to be painted again. The contractor would have specified what specific items were excluded when using general terms.

Why do you ask?

During the back and forth of contract negotiation (for a large whole house remodel), getting details on what was and was not included for painting was like pulling teeth. Earlier, we had to increase the scope for painting with a significant change order. I didn’t drill down on what was included in “trim” or thought to ask whether closets were included. I did ask (in writing) after the change order was approved: “this means the whole house will be painted... every painted surface that is not otherwise wallpapered will be freshly painted.” He replied: “yes.” At that point, I felt we had come to a meeting of the minds on the painting piece.