The term grosbeak does not refer to any specific family or genus of birds. Instead grosbeak is a term that refers to a physical feature that a number of different seed eating birds share. Although all of these birds are passerines they all belong to a different genus. For instance the pine grosebeak, pictured above, is a member of the genus Pinicola.
The evening grosbeak, pictured above, is in the same family as the pine grosbeak, Fringillidae, but is a member of the genus Coccothraustes. The genus Coccothraustes also includes the hawk finch and the hooded grosbeak. Both the pine grosbeak and evening grosbeak are closely related to finches.
The rose-breasted grosbeak, the one pictured above is an immature, is the most common grosbeak found in my area. The rose-breasted grosbeak is a member of the Cardinalidae family and is in the genus Pheucticus, which also includes the yellow, golden-bellied, black-thighed, and black-headed grosbeaks.
The blue grosbeak is also a member of the Cardinalidae family but they are found in the genus passerina. The genus passerina also includes the North American bunting species including the indigo and painted buntings. Since both the rose-breasted and blue grosbeaks are members of the Cardinalidae family they are both also related to cardinals. There are many other types of grosbeaks in a variety of different genus' found around the world but unfortunately these are the only types that I have ever found here in Minnesota.