Does iTerm (or iTerm2) on Mac allow storing host connections with user/password ( for quick access to different hosts)
Yes and no.
The usual way is to set an ssh entry as a profile in Iterm. Here is an example  for a local NAS.

The no is for the password - iTerm does not provide a way of associating the password with a login. But in practice this is not a problem as you should be using Public Key Authentication
If you are not using PKA then look at use of expect with ssh e.g. https://stackoverflow.com/a/4786000/151019
Note saying &quot;even Putty does this&quot; is a very high bar, Putty is has a lot of functionality.