'87 E150. I have done the front brakes many times.

Now originally I saw the front brake pad had material glued to the thick steel body, and a thin steel shim stuck on the surface. It didn't always stay stuck, and if I had to take it off and reassemble it later (bearing repack) it was never still stuck. Additionally, there were often a loose thin steel piece that went on top of that, maybe with little tabs on the side to try to grip the pad, sort of floating.

At least that's what it was originally. As I recall some of the sets didn't have a second floating steel shim and I guess I usually reused the ones which were there. These are a total pain since they want to fall out of place until the pedal is pressed enough to tighten it up. When reinstalling the pads for any reason, it's a total mess with 4 loose shims on a side

The most recent pads I got didn't even have the steel piece that was attached to the pad. So are what do these 2 pieces of metal do? What are they called? Do I really need them?

I was in a hurry and just put the new pads in already. I noticed on dry ground my stopping distance was a bit high, and the pedal maybe a bit squishy, but I'm thinking the pads just aren't well set yet. If that was some kind of padding between the caliper piston and the pad, it would make it stiffer to remove it, not squishy. There wasn't any rattling so if these are anti-rattling devices they don't seem needed.