There is a lot of PSU interchangeability between macs (and not limited to one side of the 68k/PPC change over), but it is important to note that the power rating tends to slowly increased with newer machines. Off the top of my head the following are can be grouped...
IIcx, IIci, IIvx, IIvi, P600, Q700, Q650, PM7100
Q610, Q660 (assumed), PM6100
Quadra 840av, PM 8100, PM8200, PM8500, PM9500 - PSUs in Italic have an extra power connector so can be used in older machines, but newer machines can't be used with earlier PSUs.
LC, LC II, LC III, LC III+, LC 475 (and equivalents).
SE, SE/30
Performa 630, Performa 6200, Performa 6300 (and each of their variants). Note - Performa 6360 specifically requires an extra voltage.
Q900, Q950, possibly the PM9150?
II, IIx, IIfx (IIfx had a two speed fan I believe).
PM8600, PM9600
PM7500, PM7200 and PM7600
Performa 6400 and PM6500
Beige G3 / Beige G3 Tower - Not interchangable between the two, this row is just for notes on using ATX PSUs - there is a jumper on the board that lets you invert the soft power logic, which allows you to use ATX PSUs. Note it is set differently on the towers and desktops, which might explain why your computer powered on as soon as the power was connected after you swapped the logic board over.
I've skipped over some stuff because it is unique (IIsi), and most Compacts / AIOs because I haven't messed with them as much. Other stuff I've probably forgotten. Additionally, in the 90s Apple made a lot of variants that were fundamentally the same computer, like the Performa 630 vs the Performa 640, or the PM 8500 vs the WGS 8550 etc. etc. etc.
Traps include...
The Quadra 800 doesn't have the same PSU as all of the other machines in that style case.
The Beige G3 doesn't have the same PSU as all of the other machines in that style case.
It feels like PM 8500/8600 and 9500/9600 boards should be interchangeable, but the power connectors (both of them, even the one that has the same number of pins) are completely different.