The bit about using the interphase phenomenon for transwarp is from Shane Johnson's Mr Scott's Guide
. It's described as a sort of a permanent micro-wormhole that the ship carries along - basically the same thing as a warp bubble, then, making distances shorter (and speeds thus seemingly faster) by perverting the nature of space.
But the name "transwarp" never applies to any specific technology in onscreen Star Trek. Rather, it seems to be the general term for anything that is better than current warp. The Borg seem to know a dozen ways to do that (all of them no doubt the result of assimilation from others); the Feds might have developed one in the 2280s, adopted it, and then set their goals at something even better.
(Of course, the terminology now also carries the "in and out of warp" meaning, as in "transwarp beaming"...)