The main difference is that MCPS license, collect monies and distribute royalties when their members’ songs are copied or synchronised to visuals (the mechanical right) and PRS do the same when their members’ songs are performed or broadcast (the performing right). It is also important to note that MCPS use PRS for Music (the operating company of PRS) to undertake their licensing activities, so when you are discussing or obtaining an MCPS licence you will mainly be dealing with PRS for Music.
