Can't seem to log in from new client

[Mike Levin]

I am running a MySQL server (v14.14) on an Apple desktop on my LAN. I can access it from localhost and from a laptop, via a MySQL client. I'm now trying to add access from another client machine and it is giving me "Failed to connect to server: Error: Access denied for user 'user2'@'machine4.localdomain' (using password: YES)" even though I've done

grant all privileges on . to 'user2'@'machine4.localdomain';

I've also tried it by IP address. No error server-side, it claims it's implemented the privilege change (and I did flush afterward) but I just can't get the client to pass the login. What might I be doing wrong and how to debug it? I can't figure out why some clients are able to connect and this new one can't.