Field of view depends on the angle the light hits the focal plane, hence why 50mm is not the same independently of focal plane size.
IRL a 50mm lens FOV ALWAYS depends on the focal plane size, just as the effect of aperture ALWAYS depends on focal plane size.
So in short, sensor size influence magnification, signal ratio (read ISO noise), field of view. The only thing in photography truly independent of sensor size, is perspective.
Technically speaking, crop sensors don’t exist, there is no such thing as "crop" in sensor sizes. What we see is the law of physics: focal plane determines the effect of the optics. That's it.
Crop means a section of. A 50mm APS-C lens doesn't give anything to crop at all, only a 50mm FF lens does that, yet both give you the exact same FOV, f-stop etc.
The term crop sensor was invented to explain the effect the new sensor sizes had with current lenses (FF film based), it was a marketing term not a scientific reality.
It's all about the angle light hits the focal plane, being film or sensor doesn't matter, the laws of physics haven't changed simply because we changed technology from film to sensors.
Some assumes a lens FOV is independent of focal plane, it isn't.
Let me give you another example. Take a canon ball of 1 kg, put it on the moon, how much does it weigh then, answer 0.17 kg. Why the canon ball didn't change at all physically, yet the property of weight did change physically. The reason is weight is a correlation between mass and gravity.
The same goes for optics a 50mm lens is relative: its properties depend on the focal plane. No crop, but physical properties are a correlation between focal length and focal plane.
As for magnification, there is no difference between how magnification works. Increasing focal length on any given sensor size magnifies. Decreasing focal plane on any given focal length also magnifies. Magnification is based on the relation between the two, hence why I said "crop" is the same as magnification, and how it works is by keeping the focal length the same and reducing focal plane size.