You've used the word "prosecuted", not "sued".

Copyright infringement tends to be a civil thing that rights holders can sue for loss of earnings, rather than a criminal thing that the police will prosecute.

In some jurisdictions the civil wrong can be tipped into a criminal offence. In England if you infringe copyright as part of a business that would be a criminal offence.

I've read that streaming might be legally different, as it might not legally qualify as making a copy. It's difficult to find a reputable online source directly answering this question. I imagine the answer might vary between jurisdictions.

Streaming definitely counts as making a copy, it is functionally the same thing as downloading the media. Search your ram/HD and the file is there. I've never heard of anyone prosecuted just for downloading though, which is what I'd guess started this rumor.

I thought it was simply that uploaders get charged with distribution which carries a stiffer penalty or something. Like the difference between getting charged with drug possession and drug trafficking. How getting caught with drugs, unless in massive quantities, will have less steep punishments than getting caught with a bunch of drugs, scales and baggies.

At least in the cases i've heard of. It could be one of those old wives tales kind of things though. I honestly don't know.