There was a time when the words cemetery and graveyard were associated to the same place. Right now, there is a slight difference in the usage of these words. When you say cemetery, this may be a large burial ground that can be placed in a large area of land.
This may not necessarily be connected to the church. When you say graveyard though, this may be near the church. This can also be the burial ground of people who had their wake at a given church. A lot of people are scared of graveyards and cemeteries because they believe that there are a lot of ghosts and other supernatural beings that may be lurking around the area.