Which application to replace Superputty / PuTTY CM in macOS
Look further into terminal before you give up on it. Under the Shell menu, you'll find New Remote Connection.... The list of default servers will be auto-populated via Bonjour, but you can still create and save new sessions for ssh, sftp, ftp, and telnet. Of course, the default services in UNIX also allow you to create your SSH keys so that when you log into a remote host, you don't have to enter your password.

You can also customize your windows with a lot of features not seen in simple Windows packages like PuTTY. Be sure to check out your Terminal > Preferences... for customizing colors, keyboards, shell commands, fonts, screen size, key mappings, terminal emulation, and a whole lot more.

Oh, you can also create new sessions in tabs, not just new windows; the second option under the Shell menu will do that.