What are the legalities of aviation photography?

Specifically in regards to commercial airlines, international and domestic flights. Are you allowed to take pictures of the planes on their route? Or just when landing/taking off at the airport? Though I know security does give a hard time at the airports too.

As an example, a park is along the flight path. The planes fly fairly low over said park with landing gear down as they are on approach to the airport. Can you take pictures there?

I am semi interested in aviation photography (since a kid been into anything with an engine) but it seems like something that is very niche and may put you on some list. lol

Legally it will typically be up to the airline, as you are in their private space (it may vary with location however).
I would expect they would have less concern about photos on route than at take off & landing when pilots & systems are far more busy.
In recent years I've not had any issues, though I vaguely remember a time when all electronic devices had to be off for take off/landing.

I get that if taking pictures at their terminal but that is also true if they are on the runway/approaching runway? Thought that would be up to the airport at that point?

Yes I wrongly assumed the question was regarding taking photos from the planes, if you're photographing the planes from the ground, you'll only likely to run into trouble if accessing areas that are restricted (or perhaps if they are military, and even that is usually fine).

Sound to me like you are from one of those litigious countries. lol

I’ve shot here (LHR) freely for many years.
Heathrow's Myrtle Avenue: A plane spotter's paradise. +Video.
www.bbc.co.uk/news/uk-england-london-18817472

I've never had an issue taking pictures outside or inside an airport (people or planes) or even inside the actual plane.

I travel a lot and not once has anyone said so much as a word to me.

Airplane mode on my phone doesn't turn off the camera, no one seems to mind photographing outside the plane. Inside I think would be another story, all sorts of privacy issues. If you photographed your children on a flight I don't think anyone would mind, an unrelated passenger with out their permission another question. This is flying into O'Hare (Chicago) on a small commercial plane from southern Illinois.