Are files encrypted with gpg compatible with pgp? What about the other way? I recently learned the very basics of the procedures of using gpg to encrypt and decrypt files. But I don't have a lot of knowledge or good understanding of cryptology theory. I also hear about pgp. Besides the obvious and confusing -- at least to me -- resemblance of the name of one to the other, are the two system compatible with each other?
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.