Synagogue is the name of a place of worship for the Judaism believers, while temple refers to worship place in general. The Hindu faith and Buddha believers, and so are the older and ancient religions all have a place to worship that is being called by the generic name of "temple". The first synagogue is believed to be in the Promised land in Jerusalem, I don't know if it is still being called "Temple", but literatures been categorized all places of worship others than of the christian faith as temple, except for Islam, who has been using the term Mosque since the beginning and applies worldwide.
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