Found this pamphlet - has the most detailed info I've seen yet.
Apparently a wedding would be considered non-public...a bar? nope.
https://www.sesac.com/media/pdf/lic/sesac12_copyrightlaw.pdf
It quotes specific court cases in plain english...some of what we would not think twice about are there...non profit events (you got paid? oops it would seem), bar charges admission but only has a jukebox license, and more.
Even a record store because not enough of their revenue was from selling music.
One detail mentioned - courts will find a person liable if they have a direct financial benefit from the infringement - so you got paid? yep, you can be held liable.
The last line of this intellectual property lawyer blog article states:
When is a ‘Private’ Music Performance Actually Public? | Panitch Schwarze Belisario & Nadel LLP
We do plenty of non-profit events that we get paid very well for. The events can be non profit. Doesn't mean every vendor has to be.
It seems quite simple to me. In the USA, It's never has been about the source of the DJ's music. It's about the venue obtaining proper licensing when needed.
CD's , mp3, streaming, record pool....all pretty much have the same restrictions in regards to being played publicly. Proper licensing still needs to be obtained.........by the venue. The venue is responsible for determining if the event is public or private and getting the correct licensing. It's nothing I've ever needed to be concerned with, or have heard any DJ ever needing to be concerned with. Except one that created the concern themselves