I've seen the "Connie Mk.IV." before in diagrams, etc. I spotted it straight away. According to what I have here they run the shorter "Avaline" engines as oposed to the previous LN64 types. I have a downloaded model somewhere.
The version next to La Forge is a "Connie" converted to Fast Cruiser Technology" as a test bed. Someone at Star Fleet woke up one morning and thought, "Hey, instead of having 4 nacelles and switching between them, like on the Chetah, Constellation, Gallant, etc. Classes, why don't we just put to seperate sets of warp coils in each nacelle and switch between each set!! It would work the same way!!"
I'm working on a kitbash of the original TOS period FCT starship test bed, the NCC 518 Hamilcar, which'll be finished one day eventually.