No, Signal Desktop is NOT the same as WhatsApp web. You still need your phone for the initial setup (same as Telegram), but after that, the desktop app is untethered until de-authentication.

Also, it has a much more praised security and cryptography than Telegram, is always encrypted (Telegram is only encrypted in secret chats) and has a much more secure codebase, with more open development (Telegram sometimes takes weeks to release source code), reproducible builds and a more transparent history.

I do use Telegram (mainly for group chats), but I treat everything posted in it as I would treat a public forum like HN.