There is no such thing as HTTPS proxy. Firefox has such naming in the menu and this is quite misleading. If we say SOCKS proxy or HTTP proxy it means the name of proxy protocol. It means the language proxy client and proxy server speaks to each other. The proxy client via proxy protocol have conversation with proxy server. By proxy protocol proxy client explain to proxy server what remote server proxy server should connect and what request it should do and forward the answer to the client.

Usually proxy client is built-in in web browsers. There is SOCKS proxy protocol. HTTP protocol was not built for proxy purpose only but it has proxy protocol capabilities. So HTTP protocol ( some of its part) can be used as proxy protocol.

THERE IS NO HTTPS proxy protocol, so there is no HTTPS proxy server.
When you see such term in the menu of web browser its quite misleading.

Actually here is the story - HTTP protocol can do proxy thing via two approaches.

The first approach proxy client send to proxy server usual HTTP requests but with modified Request-URI's. This is how web browser works with "HTTP proxy" servers.

The second approach for proxification is proxy client send HTTP CONNECT methods to proxy server.

Both cases use HTTP protocol as proxy protocol.

The first appraoch is named in browsers like "HTTP proxy". The second approach is named in browsers like "HTTPS proxy" .

So what is the difference? We use proxy protocol to ask proxy server to make the request of some other protocol to remote server. The first approach is capable to forward only HTTP requests to remote server. The second approach can be used to forward ANY protocol based on TCP - thats is SMTP,DNS, FTP , HTTPS(HTTP over TLS over TCP mostly) etc.

So why to use the first approach? When we use the first approach proxy server see and understand what we acrually want to do with the remote server. So proxy server can cache the request and the answer. When we use the second approach proxy server do not understand what we want to do with the remote server. It just gets some bytes via tcp connect from the client and forward them to remote server.

Overall - so called "HTTPS proxy" is actually "HTTP proxy" as it uses HTTP protocol as proxy protocol.