No worries, easy to not foresee every possible way in which strangers could interpret a comment!

But I think that people (at least jwr, and probably even nyc_data_geek saying "on prem") are talking about cloud (like AWS) vs. renting (or buying) servers that live in a data centre run by a company like Hetzner, which can be considered "on prem" if you're the kind of data centre client who has building access to send your own staff there to manage your servers (while still leaving everything else, possibly even legal ownership and therefore deprecation etc. to the data centre owner).

What you're thinking of - literally taking responsibility for running your own mini data centre - I think is hardly ever considered (at least in my experience), except by companies at the extremes of size. If you're as big as Facebook (not sure where the line is but obviously including some companies not AS big as Meta but still huge) then it makes sense to run your own data centres. If you're a tiny business getting less than thousands of website visits a day and where the website (or whatever is being hosted) isn't so important that a day of downtime every now and then isn't a big deal, then it's not uncommon to host from the company's office itself (just using a spare old PC or second hand cheap 1U server, maybe a cheap UPS, and just connected to the main internet connection that people in the office use, and probably managed by a single employee, or company owner, who happens to be geeky enough to think it's one or both of simple or fun to set up a basic LAMP server, or even a Windows server for its oh-so-lovely GUI).

I think no one talked about having physical server on their own premises but colocating servers in a data center or renting servers in a data center.