I think it's closer to a 4081, but it's hard to say. The only real way to find out (without asking the place where you got it, I guess) would be to get a 4081 atomizer and a 510 atomizer and try them, but that would be wasteful, especially since it might not be either. You might also try to very carefully measure the battery and compare those measurements to known battery models. Yes, the ends matter. For instance, a 510 atty won't work on a 4081 battery, etc. A 510 battery I have here is roughly 60 mm long x 9 mm wide by very quick measurement. A 4081 is fatter and probably a bit longer, but I'll have to dig one out. Well, actually, I have at least 2 different lengths, but the shorter one is probably technically for a DS or DSE103 (I think it's DSE), but they will fit the 4081 atty. I know it's confusing.