This works both ways, I have been to funerals where the actual ceremony was just for family and close friends while the wake was for everyone. I have also seen the other way round, funeral for everyone wake for family and close friends only. A lot depends on the place the 2 events are happening.
In the last funeral I went to the actual service was in a very small chapel so family and close friends only, while the wake was in a large hotel reception room with room for 150 people.