S/MIME and PGP are incompatible, but they do use similar concepts (asymmetric encryption and public key certificates).
The biggest difference is that S/MIME is based on X.509 public key infrastructure and has the same issues as with SSL: if you want a certificate that will be shown as "valid" to other users, you have to obtain one from a CA that everyone "trusts", and this costs money. The CA cannot always be trusted, too; see recent Comodo pwnage. The "X.509" page on Wikipedia has a nice list of issues.
On the other hand, in OpenPGP you create your own certificate, and validate other users' certificates using "web of trust". There are no authorities, besides yourself and your immediately trusted friends, who determine whether someone's key matches their real world identity. (This, however, can sometimes be hard to do if you don't know the person at all.) WoT is not without problems either, but (IMHO) they are smaller than those of PKI.
PGP/GPG Mostly used in *Nix ( Linux ; Unix ) Operating Systems, where e-mail clients, for example, has this feature built-in.
S/MIME is mostly used in Windows Operating systems, where it is built-in in Microsoft's E-mail client software products.
Also, from other perspective of "purpose of signing and/or encrypting email", there is interesting information in this book: "Inside Windows Server 2003. Autori: William Boswell. Page #975"
Yes, both GnuPG and the commercial PGP.com are implementations of the same OpenPGP standard; in fact, GnuPG was specifically designed to be PGP-compatible.
The only differences you might encounter are:
Different supported algorithms. For example, GnuPG supports the Camellia encryption algorithm, while PGP.com does not.
This is almost never a problem, though, as every PGP certificate ("PGP key") lists all algorithms that the owner's software supports (or more precisely those which the owner prefers to be used), so a message's sender can always pick a supported one.
Various quirks and differences in really old versions of PGP (especially the original releases from before OpenPGP was standartized). However, both GnuPG and PGP.com can easily read (if not always write) messages in the old formats.
tl;dr: Yes, they are compatible.
Best Answer
Why Use PGP? -- probably fits your size.
Would also recommend -- GnuPG FAQ Advanced Topics for a quick read
HowTo and tutorial references afterwards,
Take your pick on a comfortable read.