Aer Lingus use even numbers for east bound flights and odd for west bound.
The difference between the flight number and the ATC Callsign is to stop confusion. For example, BA may have flight BA601 and Easyjet may have flight EZY601. They may also both in the air at the same time, so if they both use the flight number as a call sign then the chance of confusion on the radio is super high and poses a safety risk, so they change it. For example (and these are made up) the BA becomes speedbird 6AB and the Easyjet 6RT.