With Amex at least you can simply provide your SSN as your EIN for your business and say you're a sole proprietor. I'd assume others work the same way. (I did this to get an Amex under a 2nd business name when I really needed to top off some miles...)

Business cards might not have the same "everyday spending" bonus points. They may have bonus points on business purchases instead. Other than that they tend to be very similar to the equivalent consumer cards.