I generated a key pair with GPG Tools for Mac and exported the public and private key to a safe place.
I assume that I can decrypt my stuff with this USB in any OS (e.g. Linux) and any GnuPG software.
Is that correct?
GPG Tools is a distribution of GnuPG with some front end and integration addons. All key management and cryptographic operations is handled by GnuPG. You can also verify this by running
gpg --list-keys on the command line, which will show the same keys the frontend tools know of.
Furthermore, GnuPG does implement the OpenPGP specification, so I'd rather call those keys "OpenPGP keys": they're also interoperable with other implementations of OpenPGP (PGP, OpenKeychain, the Monkeysphere development library, ...).