AFAIK 'Arrival' and 'Departure' are callsigns used in the US where the aerodrome approach radar service is split between multiple positions.
'Arrival' is roughly equivalent to 'Director' in the UK.
The UK equivalent of 'Departure' usually has the R/T callsign 'Control' (although internally they're known as 'Departures').
This is from observation - the pros may correct.