I'm not 100% sure, but it's my understanding that piñon/juniper is a biome rather than a species. It consists of Ponderosa and piñon pines, as well as Alligator Juniper, one-seed juniper, and rocky mountain juniper, and probably some other species of pine and juniper.
@ShadyStump probably knows more about this topic than I do.
I'm mostly only an expert at dead trees, at least when it comes to ones in pots, but you're correct; piñon juniper woodland refers to a particular sort of biome or ecosystem characterized by the symbiotic relationship between piñon pines and the various juniper species that cover the exact same range. In my region it's two needle piñon (pinus edulus) and then mostly one seed juniper, withe Rocky Mountain juniper in some spots. Get across the Continental Divide and it becomes Utah juniper. I'm personally unfamiliar with alligator juniper because it doesn't grow here. The 5 needle piñon takes over for the 2 needle as you move west to the Sierras.
The pine pictured is likely a ponderosa. They can sometimes have those shorter needles, and judging by the background of the pic sure as heck ain't piñon, not anywhere you'll find pine duff scartered like that with everything growing tall enough to be out of the picture. Piñons are short, 30 ft at the extreme, but usually half that, and close to the ground. It's rare to find one you can walk under.
To tell the difference between fir, spruce, and pine:
Pines always grow their needles in little bundles called fasicals (sp?) of 2 to 5 needles each.
Fir grow individual needles that pop out of tiny little balls on the branch.
Spruce are also individual needles, but they sit atop a little flat tongue that connects them to the branch.
There are a couple species that are commonly called spruce or fir that are actually the other. An example would be the blue spruce, which is actually a fir species, if I'm remembering correctly. I've been known to get stuff backwards.
Edit: for most things on the topic, you're much better listening to
@Colorado than me, especially collecting. My aftercare routine tends to look allot like, "oh crap, I have a tree, don't I?"
so frustrated! Thought it was and I thought I ruled fir out!!
Guess that's plant ID for you though
I'm learning to slow down I know I want to do way too much way too fast, honestly just need to get a bundle of BC from the arbor day foundation. That'll have me too busy to over work any tree 
