For me, "log in" has a very specific meaning - it's the complex process, usually interactive, that takes username and password and whatever 2FA you have and produces the session cookie.
This is pretty different from "authentication", which can mean "log in" (for new users), but also "check existing session cookie", and also "check API token", and maybe even "check trusted header from upstream authenticated proxy".
For me, "log in" has a very specific meaning - it's the complex process, usually interactive, that takes username and password and whatever 2FA you have and produces the session cookie.
This is pretty different from "authentication", which can mean "log in" (for new users), but also "check existing session cookie", and also "check API token", and maybe even "check trusted header from upstream authenticated proxy".