What is the difference between a funeral and a memorial? 

Generally speaking in Australia:
Funerals are "the ceremonies for a dead person prior to burial or cremation; obsequies".
Memorials are the ceremonies for a dead person after the burial or cremation. Many people think of memorials as on the anniversary of a death or tragedy.

However increasing in Australia, memorial ceremonies held instead of funerals, sometimes within a few weeks, sometimes a little longer if there has been a delay in the issuing of a death certificate.