Method of authorization on the site (PHP)?

Question

User identification

It seems to me that authorization is such a processor.
The user enters a username and password and sends them. On the server, they are checked against the database. If everything is OK, then the server gives the client a randomly generated key and the client writes the key to the Cookie.
Is it correct?
Are there other ways?

Answer 1

In general, everything is about the same. Details may vary.
There is essentially no alternative.

Answer 2

In general - yes, I will note:
- in addition to cookies, you can consider the session mechanism,
- in the database there is not a password, but its hash.