What's the difference between TV and cinema motion?
I don't know where they have "TV motion" from as at least in my area we use 1/(2×fps) for TV too. Or higher for sports.

1/(2×fps) simply has a "natural" motion blur to it which is often used in cinema as it is often the best choise.

A shutter slower than that has much more shutter, I describe it as dream like.
A shutter faster than that often looks like a robot, with each image being sharp and jumpy.

The first can be used in slow scenes as it won't be really notable.
The seconde one can be used in for example sports TV so you can really see each detail and it isn't blured out