Any ordained minister (as defined by their denomination or elder board) is considered a “Duel Status employee”. This basically means that they are considered self-employed AND fully employed by the church. That said, an ordained minister is allowed to consider some of their income as a “housing allowance”. Historically, some churches offered a parsonage, but those are now fairly few and far between. For the purposes of this discussion, we’re going to assume that this is a standard ordained minister.
Every non-religious, non-profit organization must file Form 1023 with the IRS. It is the application to be a non-profit. Non-religious non-profits must also do an annual tax return, Form 990.