In addition to 1:many, many:many, and many:1 (which is just 1:many but looking at it in the other direction), you also occasionally see 1:1, for example if you want to augment a table with additional data. This might be done by having your foreign key also be your primary key in the augmenting table, since that would also enforce a uniqueness constraint on the FK as a result.

Also, probably unnecessary to mention, but you can also have "0 or 1" relationship (meaning one side is optional but capped at 1). These are technically separated from "1" relationships usually when you get into all the theory. An example of this might be a "0:1" relationship using the above augment table, but where the augmenting table isn't required to have a row for every row in the augmented table. (A 1:1 constraint can be enforced, for example, by having an additional FK in the augmented table pointing to the augmenting table.)