In the case of the elevator, "trapped" and "stuck" mean pretty much the same thing. You can't get out of the elevator. You usually use "trapped" when you are unable to get out of a situation. You can be trapped in a burning house for instance. "Stuck" you use more when you are unable to make progress. You can be stuck in traffic for instance. Or you can be stuck trying to solve a riddle.

For the elevator situation they can be interchanged. But for other situations trapped = you can not make progress or require to be rescued. Stuck = you are temporarily held up. "miners get trapped in a mine when there is a collapse or explosion, and have to wait for rescuers to dig an escape route" "climbers get stuck on a mountain, when bad weather sets in, and they have to take shelter and wait for the bad weather to pass"

In your example they are basically the same. Other Examples: He set a trap for the mouse. The mouse tried to get the bait and was trapped He pushed the ring unto his finger so hard that he could not get the ring off. The ring was stuck