Seasonal Vs. Orbital years.

While reading a collection of old Sci-Fi shorts (Specifically, “Enemy Mine” from Asimov-attributed The Super Hugos), talk about one day here Vs. on Earth and seasonal weather on a blisteringly cold planet made a few odd thoughts pop into my head.
The Earth’s seasons are more directly affected by the tilt and how well we’re pointed towards the sun than the relative distance from the sun, according to what I’ve been told. I believe that the Northern Hemisphere hits Perihelion in Winter and Aphelion in Summer, counter-intuitively. Probably thanks to Copernicus, we’re at about the same spot in our orbit each corresponding day of the year, which fit the seasons perfectly.
Is that last point just pure chance, or is there some grand scientific reason for this? Are there any planets where the “seasons” fall into a schedule unrelated to their rotational orbit? If not, is it theoretically possible? If no to that, then why not?

(I’m assuming you’d tell me this anyway, but…) are my assumeds and inference correct, simplified enough that it’s impossible to tell, or altogether wrong?

Many thanks. I’d probably sit on my ass all weekend thinking about this normally, but now I can waste it on reading more Sci-fi and training the dog to scratch my back.

I’m not completely certain I understand the question, but I’ll note that the length of our year is indeed the time it takes Earth to complete on orbit around the sun, and it would be much the same even had Copernicus been a beekeeper.

On any planet, the concept of seasons is likely to be related to energy input. We get ours from the sun - probably not an unusual thing for a planet. In theory, a planet could be in a nearly circular orbit with its axis of rotation perpendicular to its orbital plane. We’d then expect little seasonal variation due to orbiting the sun. If it also had some other significant energy source subject to periodic fluctuations (a pulsating molten core?), then this might produce seasons.

No, it’s not theoretically possible for seasons to wander willy-nilly about the year. They’re dependent on the tilt of the axis, which is always pointing off to “infinity” in the same direction - in Earth’s case, pointing the North Pole almost directly at the Pole Star.

The axis of rotation is more or less fixed; a planet-sized body’s axis can’t wobble… except slowly. Ours does precess over many thousands of years, which means we get a different Pole Star in a few millennia, and the seasons will gradually shift around the year as this happens. But it’s an extremely slow process.