Your singer would possibly fit into both of these openings - provided the wider one has a big enough lip so the machine does not fall through.
Newer machines often will fit into the space the older machine + lift fit into. The main hting - the spacing for the hinges is the same for most Singers. And since the hinges are what support the back side of the machine, you do need them even if you don't intend to tip the machine down to store.
I know a 201 will fit into a cabinet that a 400 and 500 series Singer fits in, but on a lot of newer Singers, they went into cabinets that had a board the machine sat on. However those machines have a built in base so they will sit on their own. If they tip, there was a clamp to hold the machine base to the board, and the board tips, there are no hinges. So a 201 will fit - if you make a base for it to sit on.
You really need to eyeball the specific cabinet to know if it will fit if it is not an older Singer cabinet. Sometiems you may need to modify an older cabinet as the back end of the 201 extends farther because of the potted motor. I had one and the flywheel was hitting the support for the front flap and would not lower into the cabinet. On others, I've had to change where the back support block is, this is what the machine rests against when fully lowered. Some cabinets have them, some do not.