Not at all. Mentor and Tactics trainer are adaptive systems that measure your performance at taking those tests.
A Live/Online chess rating is essentially a Glicko-based system that tries to match up to your actual competitive (vs. other players) playing strength using both your rating and your opponent's ratings to come up with an updated score.
Now if your question was "do they all correlate, though?" then my answer would be "somewhat"
Are the ratings of the chess mentor, tactics trainer and live chess connected in any way?