As for the Finch discussion I think Roger Tory Peterson described the Purple Finch best "A Sparrow dipped in raspberry juice."
The red "headband" is one clear giveaway to ID'ing House Finches, Purples have a more pinkish/purple colouring all over their heads. The crown (top of the head) is more brownish in colour on a House Finch, as you will notice in the above photo. The dark streaked flanks (just below the wings on the sides of the belly) are also a fairly good indicator, Purple Finches usually have very light or no streaks on their flanks. The amount of red colouring in the feathers can vary greatly within a bird species, I've seen both ends of this colour variation at the feeders in the backyard and yes it confused the Hell out of me too!, I had the House Finches with lots of 'red' marked down as Purples for the longest time. The amount of colour on the House Finches, as well as all other bird species, is due to several factors including such things as; whether or not it is a subspecies bird, their diet, and the overall health of the bird.
Hope this helps,
Walter