first things first: When riding sw on a skateboard and popping fakie, spinning frontside isnt the same on a skateboard as on a snowboard.
here is why - when you do a half-cab/caballerial on a skateboard its the same as doing a BACKSIDE 180/360, only you are riding the other way, or switch, while popping your tail (popping fakie).
So what would logically be a fakie frontside spin is in fact called a fakie backside spin when skating.
This is (as i just mentioned) because you do the exact same thing as a ollie backside spin, you pop your tail with your backfoot, you spin "backside" BUT you are riding the other way - so even though what used to be a backside spin when riding normal becomes a frontside spin when popping fakie, we ignore the fact that we did a FRONTSIDE spin when skating and call it BACKSIDE - because physically we move our body like we would for a normal ollie backside spin...
I know it doesnt make much sense, but thats how it is for skateboarding and thats how it has been for at least 30 years.
When riding sw and popping "nollie" (sw ollie) however, this rule doesnt apply. This means that even though you are spinning in the same direction when doing a fakie spin and a sw spin - lets say you do a switch FRONTSIDE 180, when you pop fakie its called fakie BACKSIDE 180 - they are NOT both called frontside even though you spin in the same direction...
This is not the case with snowboarding. It might be because you really cant "pop fakie" on a snowboard or maybe just because it makes more sense - snowboarders do sw frontside spins the same way you do sw ollie frontside spins on a skateboard.
I hope that made sense..?
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As for skiing I couldnt care less about calling riding backwards switch or fakie but i kinda agree with the fact that no spin should be called cab...
Here is how we name our spins in Norway - its a good system that works so everyone should jump on the bandwagon...
Say you spin left, like most people do:
riding forward - Normal
Unnatural or right-side
riding backwards - Switch
Cab (switch right-side)
I hope people are able to understand this, if not, then i just wasted 20 mins of my life...