Was reading Designing Miracles (which is fantastic book by the way) and inside it Darwin Ortiz wrote about a Ultra-Mental Deck. From the description, it sounded like Invisible Deck.

Is it the same or there is a difference?

The Invisible Deck was previously known as the Ultra Mental. Old magic books also refer this deck as the Ultra Mental.

I have no idea why and when it was changed to the ID.

I guess it got the name based on the presentation of the invisible deck?
Where spectator did the selection of card, return into the deck and shuffle it based on an imaginary invisible deck

Ok, just read it somewhere that "Invisible Deck" is the name of the routine, as performed by David Blaine on his Street Magic. It is actually a way to present the effect of the deck.

The official name is Ultra Mental Deck.