Maybe. Differences are due to the limitations of energy input, and softer and easily "torn" nature of green wood. You want a sharp tool paring shavings away, never a scraping action which is harder work and leaves a grotty finish.
Some of us pole lathe turners prefer older carbon steel tools as opposed to HSS, frequently sharpened more as you might bench chisels - on a water or oilstone rather than straight from the grinder, with maybe a single flat bevel around 30 degree bevel angles rather than the steeper ones often found on power lathe tools.
I am told power lathe turners don't use flat chisels as some pole lathe turners do - a wide (2") flat, beveled on one side only, used bevel down at an angle to the work to get a smooth cylinder or gentler curves, where you might use a skew. Then there are the hook tools used for bowls and other cross-grain turning which I imagine would be quite scary to use on a power lathe ?
I am being deliberately a bit vague, as bodgers are usually not the sort to follow rules, and so there are probably almost as many opinions as turners.
Edited to add - the reciprocating action doesn't make a difference - the tool is only touching the wood on the down stroke of the treadle. You back the pressure off on the return stroke - if you don't the tool can easily be lifted off the rest and cause a catch next treadle stroke.
