The 3/8 chain for 50 to 100cc saws has larger drive links that is at least in my opinion why the mis match works one way and not the other, at a rim type drive sprocket. The center of the rivet to the sliding surface is less for the 3/8lp or picco. It has been called 3/8 reduced which would probably be more informative. I think the low profile trademarked by Oregon means the cutter top is closer to the bar sliding surface than the regular chain. They had low profile .325 33, 34,and 35 LG and SL that used the normal .325 sprockets bar and drive I think even splicing pieces as well.
It took me awhile of getting into it to fully understand what low profile meant, that it wasn't just narrower chain like some narrow kerf chains, but that the profile was lower due to less material vertically in the links, and teeth that were also quite low. By my understanding, what makes it cut (and particularly mill) so well is that due to the low profile, side to side motion is minimized more than in almost any other chain, producing an exceptionally smooth surface and relatively small effective kerf. The higher the cutting edge of the teeth is off the bar rail, the more there will be side to side deflection, so narrow kerf chains that sit at conventional height still produce a fairly big effective kerf. One person in a past thread noted that milling with .325 .063 was some of the smoothest results he'd ever had, but the kerf was about as big as standard 3/8.
Bottom chain is 3/8LP, top is 3/8. Note matched rivet spacing of both, they are both technically .365 pitch. The subtle mismatch that doesn't allow interchange is in the shape and depth of the drivers.