I might have missed something upthread but autogenerated keys to me just mean that the key is somehow generated automatically for you rather than using a natural key like social security number (SSAN) when inserting rows. Autoincrement IDs are one way of autogenerating a key that delegates generation to the DBMS server.
To expand on this, there are three common approaches to create automatic keys in SQL applications.
1.) Generate it in the application itself. You can make UUIDs yourself with a simple call in most languages. Ensuring uniqueness is your problem--to generate integers, for example, you'll need some sort of coordination if there's more than one application thread.
2.) Generate it from a SEQUENCE. Sequences are database-side key generators that hand back a unique sequence number from a block of available sequence numbers when you call for the next number. Uniqueness is pretty much guaranteed since numbers come from the shared database server. This approach is popular in PostgreSQL and Oracle.
3.) Generate it from an auto-increment column, such as MySQL AUTO_INCREMENT columns. Auto-increment columns generate the key server-side at insert time. Uniqueness is guaranteed, but you can't see the key until it has been inserted. If you need to know the key for follow-on INSERT or UPDATE commands you have to select it back using LAST_INSERT_ID(). [1] Auto-increment keys are popular in MySQL.
ORMs like Hibernate JPA tend to provide all of these as choices. I don't use ORMs much myself hence can't comment much on the details.
[1] https://dev.mysql.com/doc/refman/8.0/en/information-function...