By definition, what is the difference between a fast break, secondary break, and a transition offense?

Not sure what you are looking for... but a FAST BREAK is a traditional 2 on 1, 3 on 2, anything where the offense has numbers on the D. A SECONDAY BREAK is a numbered break where certain players will be in specific spots and post players going to the ball side block and the other post trailing..... a well organized secondary should be able to go right into your offense without having to set it up.

Does this help you?

Yes.
So a Transition Offense is a broad term for either a fast break or a secondary break, or is it an interchangeable term with a secondary break? The reason I ask is because the terms seem to be used differently depending on what resources I read.
Secondly, I keep reading in the secondary break that a post player should go to the ball side block. Is it OK to have them go to the weak side block to give the point guard an opportunity to drive to the basket for a layup or dump pass to the weak side post. If the point passes to the ball side wing/corner, then the post can flash to the ball side block.

You will find that those terms are used inconsistently. Coaches and resources tend to have a slightly different interpretation of the meaning. So you'll just have to interpret what each source means.

To me the fast break is when you get possession of the ball and you run down the floor. Then if you don't have anything you move into transition offense (which could also be called a secondary break). The transition offense is when you are "transitioning" from your fast break into your half court offense. Ideally you transition quickly and seamlessly into your half court offense without stopping or resetting.

Thanks, that helps.