An essential point is being missed here, which is that contributing directly to the welfare of people in need, as Iggy did, has little or no connection to supporting ministries. In many, perhaps most, US churches the contributions go first to supporting the church or the ministry. Some, particularly conservative (mainline) Protestant churches and Catholic churches, have established charities and they budget a percentage to them regardless of actual contributions made to the church. Many others do not.
Because most churches are tax-exempt in the US, contributions to the church or ministry also is tax-exempt. So contributions to registered churches, and contributions to registered charities, are handled the same from a tax standpoint. But the churches don't have to make any contributions on their part to charity to maintain their tax status. They can keep it all for running their own organizations. Tax-exempt charities cannot.
You can't enter someone else's head and determine their motivations for contributing to one versus the other, but their functions clearly are distinct. Whether one considers a contribution to a church to be equivalent to charity for people who are suffering the effects of a natural disaster is up to their own conscience; in some cases, it's a matter of declared church policies.