Miranda class. Ah, didn't know that Reliant was originally planned as Constitution class.
Aye, that it was. The decision was made to change it to a new design for two reason: one, the battle sequences would have been very confusing, and two, the Enterprise filming model was difficult to work with (I know Ken Ralston at ILM was on record as hating the thing). As for class names, they were still figuring that out at the time, though I believe the Reliant dedication plaque listed her as a Miranda-class.