Different.
Proper BMX shoes should be aiming for a stiff sole for the usual pedally reasons without necessarily too much in the way of drop absorbtion. More likely to find lace management features here as no one likes lace in crank. Real skate shoes should have high impact absorption for drops to flat on concrete etc. Both will likely have good levels of grip. Both will likely have reinforced toes. Occasionally you get crossover like Etnies Numbers.
Bear in mind many ‘skate’ shoes are just plain lookalike trainers, and if you’re looking to save over MTB specifics the savings aren’t as great as you may first think until you get upscale, although you can often pick up deals on less fashionable shoes like Etnies Kingpins that work very well and locate your heel well until they get wet and take days to dry out… 😉
