Hi Steve.

White deal as known here in Brit land is Pinus Sorbus a soft white timber with not a lot going for it because of its soft open grain mostly used for internal work in houses.
Red deal is the name we Brits have for Scots pine a far superior timber used for quality house parts like door casings skirting boards.
So a white deal gun case is the cheapest and usually covered with canvas.

The only lessons in my life I truly did learn from where the ones I paid for!