Test driving an FTP client with network I/O, does this fall under integration testing or functional testing?

I'm new to TDD and it's my first time to test drive a real-world project. First, I wanted to test drive an FTP client so I did. Since the FTP client naturally deals with network I/O, in my opinion, there's no use to unit test it because unit tests should not include any I/O operations but only in-memory operations [1].

The confusion lands in integration testing and functional testing though. Where should I place my FTP client test suite? The integration testing can accommodate I/O operations [1] but FTP client is only one module, so should I place it under functional testing?

[1] http://ift.tt/2f0snx6