Bee's and Tally's are the same cards, with the same finish, made by the same company with different back designs.
Bee's are used for manipulation (McBrides uses these) and for gambling routines.False dealing is way easier with Bee's.
Bee's are used in casinos, and they are very, very high quality.
Bikes have a different clear finish called "air cushion."
Cards with a white border(Tally's and Bikes) are best for most sleight of hand card magic, as the white area gives you a margin for error.
No cards look normal to people. It's the magic that looks normal. I've been looking in people houses at their cards, and I've seen dozens of different style. Most of what magicians think about playing cards is all in their heads.
Use whatever cards give you the most confidence.
Bikes and Tally Hos are not the same exact cards and if you own both kinds you can plainly see that. Tally Ho uses Linoid finish and Bikes use Air Cushion finishes.