it’s felt applied to a plastic backing. I can remember when they were made entirely of a stiff felt, without the plastic, and the centre was made up of a black dot and a smaller green dot. Now they’re only two pieces, the black dot and the felt-on-plastic. I seem to recall that the all felt ones were a darker red as well.
I remember putting the old felt ones together many (hundreds of) moons ago. The Legion brought all the parts and our class spent a few hours doing red, black, green, pin! over and over. It was better than Social Studies at least. 
Yeah, it might be a heavily regional thing in the US … and I’m wondering if there isn’t some North-South dichotomy going on (I am in Louisiana). There is a VFW hall a few blocks from my old high school, and I still never saw the poppies.
I always buy poppies from vets, usually outside my Trader Joe’s. I’ll go looking for them today.
For what it’s worth, I’ve lived in San Diego, Seattle, Connecticut, Tennessee, Illinois, and Virginia, and I’d never seen anyone wearing a poppy until I went to Victoria, BC this weekend. And for many of my years, I’ve lived either on or near Naval bases. The poppy as a sign of remembrance just isn’t common in the US.