The attachments on most old Singers *are* Greist. Greist made attachments for just about everyone and still did until fairly recently.
Like Nancy says, as long as you know your machine's needle homing position and type of attachment, you should be able to use Greist or any other brand.
There are more types than that site listed though - a super high shank from the 70's, a back-clamping from the early 20th century and a top-clamping from the turn of the century that seems to have come in at least two different heights that are roughly "low shank."
There are also attachments made for zig-zag machines and attachments made for straight-stitch-only machines.