Yep. We're meant to think it's just one saber, even though there are two very different-looking hero sabers in the film.
I blame it all on the placement of the triangle belt attachment thing on the V1. It's placed on the pommel cube that's right in line with the control box, so anyone wearing the V1 would have the control box constantly digging into their leg. The V2 had its D-ring on a different bit of the pommel, so it was much more comfortable to wear, not to mention it looked better since you could see the control box.
EDIT: Oh, and here is the reason that the V2 has the cone attachment:
The Obi ANH stunt saber is the Luke V2. The Cone knob was added to the hole left when the on/off switch was removed (since the sabers with blades in ANH had motors that spun the 3-sided blades covered in reflective tape to make them appear to glow, although they decided to rotoscope the special effects in later).