Open a terminal on a remote computer?
I think you're just confusing some of the concepts here. When you SSH to another computer you're connecting to it in an interactive terminal. You can run commands logged into another computer through this SSH connection.

Example

Here I'm logged into my Macbook (unagi) as myself (smingolelli).

$ hostname
unagi

$ whoami
smingolelli


Now we SSH to another computer on my LAN (mulder) as another user that's local to that system (root).

$ ssh mulder.bub.lan -l root
Last login: Sun Apr 21 23:05:32 2019 from 192.168.1.95

$ hostname
mulder.bub.lan


When I'm done I simply exit this interactive SSH connection to another host and I'm back on my original Macbook host.

$ exit