Yes they do - that's why I know how low the ratings mostly are.
Horsepower is marketing, torque gets stuff done...
I really couldn't tell ya what a single saw I have horsepower rating is...I have probably read some of them off spec pages, but promptly forgotten them. The bigger the saw the mo powah it haz....
I know once you get into ported saws, and who/what/when/where how it was ported, etc, perceived and actual power can vary greatly, but....it's sorta silly, too. Any modern type saw of X-displacement will cut within it's design/size parameters, they are all going to be close, so it gets down to how much loot ya got to spend on your saws, what color plastics you like, etc. At the end of the day, just talking firewood, saw time is the least amount of time involved in the total processing of the wood, from standing tree to split wood inj the stacks. all the other steps are way more important and usually way more expensive, trucks/tractor4s/splitters, other assorted wood wrangling equipment. You might spend an extra five minutes cutting with some whizzbang hotrod saw compared to a similar sized stock saw. Whoopedy zingaroo there.
For most of us who cut just for ourselves, smallish quantities per year....factory OEM hotrod or aftermarket hotrodded saws are just cheap thrills, funzies. I got some, fun! Do I absolutely need them? Nope...Will a lb or two in my hands matter during an afternoon firewooding session? Nope....The blocks of wood off the trunk are WAY heavier usually, ha!
Anyone's 60 cc saw is gonna fill up the back of a pickup pretty quickly, any brand, stock or modded..