The Beatles (bless 'em) were a rock band. They were a boy band prototype, I guess, but not an actual boy band. I think the distinction between boy band and actual band is whether or not they made all the sounds you hear. The Jonas Brothers were a boy band because none of them played the drums. The Beatles had Ringo (groan of general reluctance). Therefore, an actual band. 

Boy Bands:                                Bands:
The Jonas Brothers                        The Beatles
One Direction                             Fall Out Boy
NSync                                     5 Seconds of Summer

The content of their songs and the quality of the band is besides to point. Take 5SOS for example. ;P

EDIT: Joe didn't really play any instrument. He should have stepped up and learned the drums. Joe. >:[

EDIT EDIT: [@Treue] Take your time. There's no rush. :)