Hi Niloc and The Observer,
I'm by far no expert in bird identification but this is what I've learned so far...
Your bird in question is infact a House Finch. The red "headband" is a clear giveaway, Purples have red (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 your first 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 them 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. Colouring is not always the best indicator of a species. Hope this helps you.
Happy Birding!
Walter
Any comments, suggestions, or criticism always welcomed.