If you're an American you will probably be astonished to discover that the US has several Public Service Broadcasters, you might know them as "the big networks", if you're old enough you might remember receiving them, especially in poorer households by just purchasing (or renting) a TV set and there they are. No subscription, no cable feed, everybody can receive them.

They use a public resource (the radio spectrum) to broadcast television, in exchange for access to this spectrum the government sets requirements on what they can broadcast and so they are not simply ordinary for-profit companies.

If you think back to the last time you heard about the Eurovision Song Contest, the reason Eurovision exists is PSBs. The right to broadcast TV in European countries is held by a large number of distinct PSBs. The reason the ESC has weird breaks in it, if you watch it as a pristine video rather than from a source which makes that obvious, is that it's intended to be broken up with lots of commercials in most countries where - just like a US network, the PSBs are actually for-profit entities just under constraint of law because they use this scarce public resource.

Most of the Eurovision members have requirements on proportion of local content (no trouble in the US, but a for-profit Greek company may find English language sitcoms bought from North America, Britain or Australia are cheaper than making their own), news or current affairs coverage (the actual news isn't profitable since you can get that anywhere, so a profit seeking entity would rather not have a nightly hour-long news show), and children's programming (not very profitable in most European countries since advertising to children is very heavily constrained as kids are easy to manipulate).

Correct: it's public service without being public-funded. Channel 4 is ad-funded but because they're publicly owned they don't have turning a profit as the central reason to exist. That almost certainly would change if they were sold.