Friend with benefits (sort of) is confusing me!?

From what you've written here, I'd say T is just being a friend. However, I have to agree with him. You should break up with C because you're not being fair to either him or yourself. You're obviously not commited to this relationship and isn't it about time to let it go so you can both move on with your lives? I know it's hard but it will be best in the long run. C will eventually find out about T ... boyfriends/husbands almost always do ... eventually. Cut the cord now ... and be happy!