When someone writes and records a song, she gets a bundle of rights. Those rights include copying the work, preparing derivative works, distributing the song by sale, and performing the work publicly, among others.
All of these rights are separate and unless specifically stated, a license to download a song does not also include the right to play that song publicly, like in a restaurant.
If you own a restaurant or store that plays music, you may want look into either obtaining a license for public performances from a clearinghouse such as ASCAP or BMI, or using a service that has pre-cleared the performance rights, like Pandora for Business.
If you get a letter from ASCAP or BMI demanding that you take a license, consult with an attorney.