Small birds like sparrows get around by hopping on two feet together, while most bigger birds walk step by step on their feet. Ornithologically speaking, is there a genus name for these two types of birds?

http://www.stanfordalumni.org/birdsite/text/essays/Walking_vs_Hopping.html discusses the two methods and points out that not all members in a type of bird move the same way.

Another ornithological term for Sparrows is 'passerines' or perching birds. This is a huge genus and includes the little songbirds that hop.
The 'waddlers' include the genus 'corvids' such as Rooks,Crows,Jays, Magpies etc.
More of the 'waddlers' and 'walkers' come under the 'raptor' genus. These are the Buzzards, Ospreys, Eagles and all birds of prey.

Most passerines do hop, but some varieties such as larks, meadowlarks, pipits, and starlings stride.