A .pfx includes both the public and private key for the associated certificate (NEVER share this outside your organization); it can be used for TLS/SSL on web site, for digitally signing messages or authorization tokens, or for authenticating to a partner system. A .cer file only has the public key (this is what you typically exchange with integration partners); it can be used to verify tokens or client authentication requests, and it is what is received by an HTTP client from a server in the SSL handshake.
