Specifically they're different because of the pragmatic conversation rule that direct statements should be something your conversation partner will accept, in most normal conversations. You say "X" when you expect your conversation partner to say something like "oh cool, I didn't know that." You say "I believe X" when they may disagree and your arguments will come later or not at all. "It's true that X" is more complicated; one example of use would be after the proposition X has already come up in conversation as a belief and you want to state it as a fact.

A: "I hear that lots of people are saying the sky is blue." B: "The sky is blue."

The above sounds weird. (Unless you are imagining it with emphasis on "is" which is another way to put emphasis on the truth of the proposition.) "The sky is blue" is being stated without signaling its relationship to the previous conversation so it sounds like new information; A will expect some new proposition and be briefly confused; it sounds like echolalia rather than an answer.

B: "The sky really is blue.

or

B: "It's actually true that the sky is blue."

sounds better in this context.