All Bitcoin wallets are interoperable, so your customers can pay you in Bitcoin no matter which wallet they use.
Bitcoin-only wallets:
These are pure Bitcoin wallets that unlock the full benefits of Bitcoin: no middlemen, low fees, and no chargebacks or fraud.
Hybrid wallets:
These allow you to exchange any portion of your Bitcoin for dollars as soon as a customer pays you. Fees are still less than credit card payments, but higher than pure Bitcoin payments.
Both are great ways to accept Bitcoin. The specific wallet you use will depend on the size and type of your business.