If SSL was developed for web servers, it can be used to encrypt any protocol by encapsulating it inside SSL. This is used in IMAPS, POPS, SMTPS,... These secure protocols will used a different port than their insecure version. SSL can also be used to encrypt any transaction, there is no need to be in direct (live) contact with the recipient. S/Mime is such protocol, it encapsulate an encrypted message inside a standard e-mail. The message is encrypted using the public key of the recipient. If you are not online with the recipient then you must know its public key. Either you get it from its web site, from a repository, or you request the recipient to e-mail you its public key and certificate (to ensure you are speaking to the right recipient).
In a reverse order, the browser can send its own signed certificate to the web server, as a mean of authentication. But everybody can get the browser certificate on the CA web site. Yes, but the signed certificate has been sent encrypted with the private key, that only the public key can decrypt.