The Synagogue was primarily a teaching ministry – worshipping God by the rituals of reading, repeating, and teaching his Word.
The Temple was primarily a sacrificial ministry – worshipping God by the rituals of songs, offerings, and eating.
The Church in Acts embraced both (Acts 2:42) with the “Breaking of Bread” (Eucharist) as their Temple sacrifice and “Apostles’ teaching” as their synagogue.
Whereas the Temple of Israel was singular for a singular covenant people, Christ has torn down the curtain and opened up the Temple for the world. And since the Day of Pentecost, the Temple has been multiplied to spread throughout the world.