Traditional bird taxonomy grouped colourful New World songbirds with fruit-eating habits as tanagers, family Thraupidae. Molecular phylogenetics rearranged that assembly. Piranga, which contains the scarlet, summer and western tanagers, resolved within Cardinalidae, the family of cardinals, grosbeaks and buntings, rather than with the true tanagers of the tropics.
The morphology had hinted at it. Piranga bills are stout and notched, closer to a cardinal's seed-and-insect tool than to the fine bills of many thraupid tanagers, and the song is a burry, robin-like phrasing quite unlike tropical tanager song. The English name stayed because common names track history, not phylogeny.
The conservation point is about forest size rather than forest presence. Scarlet tanagers breed most successfully in large unfragmented tracts. Small woodlots expose nests to brown-headed cowbird parasitism and to edge predators, so a landscape can retain plenty of trees while losing the interior conditions the species needs.