TMP enterprise is definitely the same ship, just refit. I don't buy the TMP Enterprise refit scrapping the original Enterprise completely, and here's why.
While the expense of upgrading the Enterprise really wouldn't be cost effective, in TMP isn't it alluded to in TMP that Admiral Kirk used his influence to refit the Enterprise, with Decker overseeing the refit personally?
With Kirk being a hero that literally had saved countless millions throughout his career as captain, including possibly saving Earth itself at least twice in the Doomsday Machine (it was headed to the heart of the Federation...or Earth?)and Changeling (Nomad would have surely made its way to Earth like V'ger),surely once he was an Admiral, he had exercised a lot of influence. Many in Starfleet and the Federation would have felt a certain amount of gratitude towards Kirk, like they did after Star Trek 4 (which they granted him captaincy of Enterprise-A).
So, is it so hard to think that someone with that kind of record that requested the refit of Enterprise, a famous ship not just under Kirk but also Pike (and April if you count TAS), would have that request fulfilled? Even if to just indulge him one last time?
Not to mention, Enterprise became a training vessel by TWOK, and probably would have remained so indefinitely until it sustained so much damage to require another refit in TWOK, much like the USS Constitution is today.