Yes, there is a difference. Several differences, in fact!
Kodak HIE has the "deepest" sensitivity, it extends farther into the infrared than any of the others. It also has the coarsest grain. Konica IR750 and MACO 820c have less IR sensitivity, but a lot finer grain. They are also slower than Kodak's. I have used both of these with very good results. They also have the advantage of being available in other sizes than 35mm.
The characteristic look of HIE is partly due to halation (spreading of light within the film), since it doesn't have an anti-halation layer. MACO make a version with the same effect, MACO 820c "AURA". I have only tried this in 4x5", where the effect is unnoticable due to the larger film.
Any developer will work; it all depends on what you prefer. I have used Ilford DDX, Pyrocat HD and FX-2 with good results on both MACO and Konica. I haven't used Kodak HIE, since I rarely use 35mm.
I know that some people use IR in studio with strobes, but I haven't tried this myself.