S/MIME and PGP are based on public-key encryption. Both can be used to signed emails. Both can be used for end-to-end encryption of emails. However, with PGP, the public keys must be mutually signed and exchanged. With S/MIME technology, an infrastructure for certificates and publication is required that is often used in B2B (business-to-business) and B2C (business-to-customer) situations. A user controls the cryptographic key in S/MIME and can choose whether to use it or not for each individual message. Email programs, like Outlook, look for the location of a trustworthy CA (certificate authority) in order to carry out a digital signature and to verify this signature. While PGP, users mutually sign each others' public keys, this is carried out by a central certification authority with S/MIME. These authorities do not sign the public keys, but the certificates, as a certificate always includes the public key with the respective identity.
Please note that S/MIME and PGP are not compatible with each other. Recipients and senders using different technologies cannot exchange signed or encrypted emails. As S/MIME is highly compatible with leading email clients and the exchange of keys is somewhat easier than with PGP, the S/MIME technnology has established itself as the stronger industry standard. PGP, which is free of charge, is often used by tech-savvy people in a private environment, while companies and organizations are more likely to opt for S/MIME.