There are two ways of signing/encrypting email with PGP:
Inline-PGP and PGP/MIME.
Inline PGP takes a plain text message, and signs it or encrypts it, and the signed or encrypted message is sent as a single plain text message.
PGP/MIME uses a MIME-type of either multipart/signed (or for encrypted mails multipart/encrypted.) The original unsigned message is left alone, and an additional MIME part is added which contains the signature. This would MIME part would be seen by any non-PGP-aware MUA as being just some random attachment.
The difference between PGP and S/MIME is more in the formatting of the certificates, and the trust model used. PGP uses a web-of-trust, and S/MIME uses a PKI based on Certification Authorities. A PGP public key file is formatted very differently from an X.509 certificate.
In terms of mixing PGP and S/MIME, its possible to do, if you use inline-PGP, and then S/MIME sign the message. (Why one would want to is another question.)