You need an adapter to handle some of the electronic differences. Many Beachtek adapters provide this. My Beachtek handles XLR to mini on 2 channels (my camera has mini plug connections, but some of my wireless mic gear is XLR). It also has switches for sound system inputs (Line) on each channel.
Your last question,
If you have a cordless mic how does the camera pick up audio directly.
seems a little unclear to me. If you have a cordless mic, it connects to a transmitter, usually worn by the subject. You also have a receiver, usually mounted to the camera, which brings the signal into the camera. If this receiver has XLR connections and your camera only has mini connectors, you use an adapter, like the Beachtek, which has the added plus of volume controls for each channel.
I hope this helps.