Werewolves or coyotes, are classified as betas simply by mutual and accepting affiliation with an alpha or another experienced beta, or as an accepted member of a pack. They gain a mystical symbiotic bond, thus becoming more powerful, more capable and mature as were-creatures.
Out of necessity and convenience, Scott and Derek worked together to stop Peter and so they were classified as betas.
Like Alphas, they are able to fully transform their bodies further into more anthropomorphic shapes, or even Evolve and transform into a full wolf as in the case of Derek Hale. However, this is harder, more challenging for them to accomplish because they lack the spark of power an alpha possesses that supplements the ability to do so.
If a beta were to dissassociate themselves from a pack, their ability would accordingly diminish. They would then be classified as omegas.