Manure, compost. Whats the difference?

Hey expert gardeners!!

I just taken on new allotment which, as expected, is pretty overgrown 
with bindweed n couch grass n stuff I don't recognise.

So, I started double digging the whole plot to remove as much as 
possible of all of these deep rooted perennial nasties.. It will take me 
until end of August to complete this.

Some people say I should then cover the dug ground with rotted manure 
and leave it over winter.   Others say I should cover it with compost. 
But I don't know the difference between rotted manure and compost?

Are they the same thing?

Ed