Often it's the location and type of hinge pin (the part that attaches the machine to the base) that are different, along with the size of the base. Some, like Davis, have the belt on the outside of the flywheel while most others have it on the inside.
The other problem is some cabinets are set up to tip the machine backward, and some nose down, while a few keep the machine level when lowered. Singers are made to tip forward and do not have any built in part to secure the front of the machine to the cabinet, while some have a screw and many have a latch.
I've also found that the pins come in several variations in diameter, shape (some are more square, some round) length and some have indentations. And the different machines have different holes they fit into. Some older ones that were not meant to be tipped (like for coffin top cabinets) don't have holes for set screws, so there is not way to secure the machine to the hinge pins.
As to getting machines to fit a cabinet, you can almost always modify the top to make the machine fit - with the exception of putting a Singer in a back tilting cabinet unless you can figure out a way to secure the front edge.
I'm modifying one treadle cabinet so I can put a lot of machines in it - but the opening accepts a base that will stay with the machine, and the bases are made so that the machine fits in them correctly so the belt will line up. This cabinet is not intended for storage of machines, though it's the type the machine would stay upright and lower into the cabinet.
If things go as planned, I'm going to have several "new to me" treadle cabinets tonight, and then I can look over them and see how the vary.
I have treadle cabinets for White, Standard, Domestic (early) Demorest, Florence (high arm), Foley & Williams, Free, Singer (lots) and will be adding a New Home (along with more of what I already have). I also have several other MFG machines without cabinets, so I can check them over for pin location and pin type.