David Sibley’s regular column “ID Toolkit” is a popular part of every issue of BirdWatching. In our November-December 2016 issue, he offered tips for identifying Purple Finch and House Finch. For further help distinguishing these birds, please flip through this slideshow.
And here's another point of distinction between the species: Some male House Finches, like the one above, photographed by Cecil Holmes in Huntsville, Alabama, aren't red at all. They're orange, or even yellow. Purple Finches are never that color.