I have noticed that my online-and live chess ratings are much lower than my Tacitcs Trainer rating. Why? Shouldn't they be equal? Or am I not the only one to experience it? In TT my top rating was around 1900, but I can never play such strongly. Can the problem be that in TT I know that there's a trick in the position, while in a game I don't always look for it?

That could be part of the reason yes. Other part could be ur decent at tactics but lacking in other area's and that's why ur rating isn't higher. Just a thought. :-)

You are having a big misunderstanding of what your tactics trainer rating means. The rating is just a tool to track your progress at tactics training.

You could have a 2500 rating at tactics trainer and have literally no idea how to conduct a game of chess. There is a lot more to chess than seeing combinations.