No. Disregarding technicalities of which there are many, the most important difference is that with ssh you either get the host key through a different secure channel or "trust on first use" (TOFU). With HTTPS you trust certificate authorities (CA).
I was referring to the browser side certificate that can be generated using the <keygen> tag, and then used for the subsequent HTTPS sessions. Would this be equivalent to ssh-keygen for SSH?
That's deprecated though and afaik, that's only the client-side authentication, not the server-side. That still relies on CAs, with all the disadvantages.
