Is there any difference between buying a cold air intake system from an auto shop,  and just running a regular intake from an area further away from the engine? 

Probably not if you can design something the right size.

What sort of car?? The KE70 pulls air from the mudguard usually, not in the engine bay at all.

I made the whole air cleaner box and put a cold air tube to the front by the headlight- a bit of 65mm plastic downpipe.  Worked so well I had to relieve the pressure in the airbox with a flap that lifts up at speed, or it would lean out the carbs. One thing it did demonstrate was just how much air the motor swallows. The flap would be closed in say, 3rd gear accelerating, then as I throttled off to change to 4th it would pop open, then slam shut as I accelerated again.

The limiting factor in that engine is the carburation, the air inlet system can feed more than the carbs can use.

https://www.rollaclub.com/board/topic/42407-the-girls-ke70/