correlator is a mixer that multiplies the signal with the carrier which is coherent system "i.e. the pilot carrier is sent along the data", while matched filter is a filter that has some equation with respect to the sent pulse " i think it was K*(g(T-t)) i am not sure about the equation , but its idea is that it samples the signal at time T ,which gives maximum SNR which makes a non-coherent system"i.e. the data is sent alone".
if every thing is ideal they have the same function with max. SNR at o/p.
i am not that sure , but this is what i could remember so re-check it.
regards,
a.safwat