Translation:The old cemetery is behind the church.
Is there any difference (meaning) in English between cemetery and grave yard?
The short answer: no.
The long answer: It seems in old usage, the choice depended on if it is next to a church or not. I don't know how important it used to be in the past, but most native English speakers today do not care or notice the difference at all. So only if you cared to be exactly 100% formally correct (for ceremonial or important purposes) there is a real difference.
In Australia we use cemetery and more recently 'Memorial Park'. You will find many differences in the names of common things depending on the English region you are visiting... shop/store, pavement/sidewalk, autumn/fall, as well as different spellings for words cheque/check, neighbour/neighbor.
Strictly a "cemetery" is separate from a church. So if it is behind the church it is a "graveyard".
"Temető" and "cemetery" sound similar enough that you'd think there is some etymological connection. That doesn't seem to be the case, but the similarity may make it easier remembering the word.
I think they just say "templom" but use an adjective. My father called the synagogue in his town the "zsidó templom"
When been taken around the Jewish quarter our guide used "zsinagoga" - but non-Jewish people seem to use "zsidó templom".