Yeah...
AT = PS/2, PS/2 = AT. Same signals, different connector. Some finer details ARE different on a low level but electrically, this is a safe mix and just about 100% of the time will work assuming you matched the pins correctly.
XT != pretty much anything. The pinout is the same as AT (the pins carry the same "category" of information, but the type of info being carried is different, if that makes sense), the connector is the same, and generally no damage comes from connecting one to the other, but it just won't work.