system
A chat on subreddit /r/NoStupidQuestions
human
If I understand correctly churches take in money then spend, give it away however they please with no oversight. Other non-profits might not pay taxes but there is oversight, they can't spend their money however they please, like say on super cars and private jets.
gpt
Churches have oversight they need to meet IRS requirements that their spending be for one of the purposes outlined in Internal Revenue 26 USC section 501 item C sub part 3:

&gt;Corporations, and any community chest, fund, or foundation, organized and operated exclusively for religious, charitable, scientific, testing for public safety, literary, or educational purposes, or to foster national or international amateur sports competition (but only if no part of its activities involve the provision of athletic facilities or equipment), or for the prevention of cruelty to children or animals, no part of the net earnings of which inures to the benefit of any private shareholder or individual, no substantial part of the activities of which is carrying on propaganda, or otherwise attempting, to influence legislation (except as otherwise provided in subsection (h)), and which does not participate in, or intervene in (including the publishing or distributing of statements), any political campaign on behalf of (or in opposition to) any candidate for public office.

For groups of this kind that need them, they're allowed to spend their money on private planes (a pretty obvious example is sending relief supplies to an island hit by a recent hurricane--there's a pretty obvious charitable use) but sending an organization's executives to many locations in quick succession to fulfill their educational mission or foster national or international sports competition is generally allowed, too.  Non-profits aren't supposed to use their private jets to fly the executives to vacations, but it can be tricky to separate vacation from mission activities (let's say an organization organized for improving teachers ability to teach the color blind performs a workshop in Honolulu in January and flies its staff to Honolulu to run the workshop is that a vacation or mission spending? does your answer change if the staff happens to take a week of vacation after the workshop is completed, etc).

Churches benefit from religious being one of the broad spending items outlined in that paragraph.  Generally, that means all the staff's salaries are going to be counted as religious spending.  The IRS makes all charities have an independent board (meaning limited family members of executive staff on the board) but they can't force the board to not overpay staff, either.