Yeah... based on the description above, it sounds like a sequel, not a remake.
Which is fine, but if you want to make a sequel, just call it a sequel. That was what I didn't like about the new "Friday the 13th" -- it would have been perfectly acceptable if they'd just called it "Friday the 13th Part 12," because that's what it was. It wasn't a remake, it was just another in a long line of Jason flicks.