It doesn't matter what you call it, any of those things, including pulling over the driver, require probable cause.
PC is not so easily defined. "Suspicious behaviour" or activity can be probable cause. Not saying I agree or like it, but it is used a lot.
If I were stopped (in the US or here) by a police officer who asked me "where are you coming from now" I wouldn't answer. I don't know what if anything he is fishing for, and as long as a citizen not doing anything wrong, it isn't their business. But as a younger man, travelling around with a backpack, or just when I was living somewhere have often been stopped. In the US it is suspicious in a suburb if you are just walking around, depending on when and where, and how you "look" and that shouldn't be, but is.
But police have many ways to explain later to a judge what prompted their suspicions. Sometimes they win them over, sometimes not.
That's all after the fact. You can see many videos of police getting suspicious and interviewing folks who are doing nothing wrong.
Then too, pulling over a driver is a piece of cake for them now that they have all hit on "improper lane change", or weaving, or any number of very iffy "judgements" on a driver that the driver is not likely to be able to counter or prove otherwise on. It's all in the setting. Nerves about school shootings I would be pretty sure driving around and around a school building (which in a city wouldn't even be noticed but is very noticeable in a suburb often) might get you checked out by cops.
My point was just that anyone showing "too much" interest these days seem to be seen as "fair game" by police to check out. Not saying it is right, but it is happening.
I don't think many of them are successfully getting sued for infringement.