They are separate characters, never confuse them. However, I wouldn't say they are mutually exclusive in skill. Improving your Fox can and probably will improve your Falco.
However, each has their own technical nook, so just because you can waveshine with Fox like a beast doesn't mean you can do it with Falco (their shine timing is much different). Fox is the most technically demanding character tho, and Falco is one of the top technical characters as well, so by merely increasing tech skill, you'll get better.
They also share similar concepts, such as: when to fire vs illusion, laser use (although starkly different, similar), quick pressure, and fast falling nature.
Practice with the one you're more comfortable with, and keep the other for spare practice when you tire out or just want a different feel. Backup characters are great for counter picking, but only if you are confident in your abilities with them.