There are basically three different types of sewing machine shanks available, depending on the type of sewing machine you have. If you are going to buy generic feet or attachments from a catalog or online, you must identify which type of shank you have on your machine.
Most machines take a low shank. This is the type I have on my Pfaff, Husqvarna and Singer Featherweight, as well as my Singer treadle. The vast majority of sewing machines have this type of shank.
This is a diagram of a low shank.
The next type of shank is the high shank. Not as many machines have this type of shank. I believe Bernina is one of them.
Here is a diagram of a high shank.
The last type of shank, and the least common, is the slant shank. This was only used for a short time during the sixties for certain Singer sewing machines.
My mother still has one and I used to sew on it when I lived at home. It only takes feet and attachments for those particular models of Singer. Newer Singer machines have gone back to a regular low shank.
Here is a diagram of a Singer Slant Shank.
Kenmore is a type of machine that has super-high shanks. Sometimes you can get adapters for these types of shanks by special order.
Be sure you identify the correct type of shank for your machine, otherwise the generic feet or attachments you buy will not fit your machine.