So they used the actual ESB helmet, but it was not in this condition during the filming of ESB?
Yes! Although the ESB helmet already had some minor damage during the filming of Empire, the helmet gets more damage before the filming of Jedi, when it was casted to produce at least 2 stunt helmets, and it is possible that for this reason (the heavy damage on the left side) they didn't used it in ROTJ. The 2 ESB style stunt helmets (also called as ROTJ stunt helmets) appear in some of the stunt scenes (the sail barge and the skiff scenes), and after 13-14 years later the damaged/repaired ESB helmet 'finally' appear in the ROTJ SE (as new addition) with a ROTJ-like armor (not the ROTJ Hero parts, but some back-up pieces).