Like the author, I frequently get hung up on which of "log in", "sign in", or any of their variants is 'more correct' every time I put together software with users.
"Authenticate" might be the most correct verb, although it's not very user friendly?
"Authenticate" might be the most correct verb, although it's not very user friendly?
Both "log in" and "sign in" are anachronisms though - they're justified when you're actually signing-in-and-out of a computer system or building to log your visit, but the metaphor doesn't technically make as much sense when you're talking about authenticating the user on a website.
The evolution of the terms does let you nicely abstract away the actual mechanism of authentication for a user, which I suppose is the point.
That is what many systems will do when you "log in", so to me that makes the most sense.
Use "log in" and "register". Don't make me think.