Your description is basically correct.

You send your traffic to a server belonging to someone else (from your home IP)

They send it wherever you want it to go (from their server IP)

The website you are requesting, sees the server IP, not your home IP

You are supposed to trust (you cannot verify) that this server (or their hosting provider) does not log all that traffic against your IP

fyi there's a new service coming up that can potentially make all this a lot more private: #101399