When you type "tmux" into a terminal, that starts a client. A client is the instance of tmux that's running in your terminal emulator. tmux manages a collection of pseudoterminals, and clients display whatever is going on in that collection.

(Warning: some oversimplifications.) This collection of pty's is called a session. Each pty within it is called a window. When you start, there will be one session containing one window. You can add more windows (C-b c) and switch the one your client is currently viewing (C-b p, C-b n, etc.) Each new window will start a shell that you can use to run programs independently.

Detaching (C-b d) means disconnecting your client from the session and exiting. Attaching ("tmux attach") reconnects to the session.

Multiple sessions and multiple clients are an advanced topic. Don't worry about them yet.

Unix sessions are unrelated to tmux sessions. Technically, each pty managed by tmux has its own Unix session.

Buffers and panes are advanced topics. Buffers help with copying and pasting; panes let you split windows into multiple pty's. Don't worry about either of them yet.