In the United States, most churches are open to anyone who wants to come in, but often being a "member" of the church requires providing some form of formal support, such as tithing (members typically have at least some say in church policy, while random congregants do not). Congregants (who may not be official members) also generally add something to the collection plate when it comes around.
Some countries still have "established" churches, which historically received direct government support from tax money (this is not always the case today... while the Church of England is still the "established" church in England, it no longer receives direct taxpayer support). Others may have a group of recognized churches that can receive taxpayer support (Germany is that way, I believe... you declare your religious affiliation, and if it is on the government-approved list, the government tax authorities will collect the tax and remit it to the church).
Some countries still have "established" churches, which historically received direct government support from tax money (this is not always the case today... while the Church of England is still the "established" church in England, it no longer receives direct taxpayer support). Others may have a group of recognized churches that can receive taxpayer support (Germany is that way, I believe... you declare your religious affiliation, and if it is on the government-approved list, the government tax authorities will collect the tax and remit it to the church).