Difference between a temple and a church

Most religious orders have places of worship. Temples and churches are probably the two most common terms. Christians have churches, Hindus and some others have temples.

Mormons (the Church of Jesus Christ of Latter Day Saints) have both - Temples and Churches. They both serve different purposes. Mormon Churches are for public worship, and anyone can go in. Mormon Temples are for private worship, and have restricted attendance.

Does this definition apply to Hindu Temples and other Christian Churches too? While people use Churches for private worship too, their main purpose is public worship - usually the once-a-week Sunday service. And, while people use Hindu Temples for public worship too, their main purpose is private worship.

Does this also underscore a difference between religions? Hinduism is primarily focused on private worship, and Christianity on public or group worship?

And, what about Mosques and Synagogues? I don't know enough to say whether they are for public or private worship. The dictionary states them both as houses of worship.