The two nebula catalogues NGC and IC are
complementary, i.e. they don't have1
any nebulae in common.  For example, the North America Nebula is called
`NGC 7000' and the Orion Nebula is 'NGC 1976'.  The
IC catalogue usually contains fainter objects.
   
Parallel to that there is the much older and much smaller Messier
catalogue, abbreviated `M'.  For example, the Orion Nebula can also
be called 'M 42', whereas the North America Nebula isn't included
in Messier's catalogue.
   
Pay attention to