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I got my hands on a 800 MHz Receiver/Transmitter. I haven't seen a board like this before, or the other part. How do these get classified?

The boards are technically called silver etch boards.
In this case a very sloppy (by standards) reverse etch. Good for you.
Depending on the thickness Boardsort will take them somewhere between low grade and telco. But there is no way to know from them until it's in the warehouse and they can scan it with a pm tester.
On the low end You've got a nickel-tin alloy know as cb flash. The boards run 15-30c/lb

On the high side (and telco range) a nickel-silver or copper-silver-tin alloy that's immersion dipped and worth $4-6 per pound.

The boards themselves are a wood and plastic pressed powder. (Education game...crack the corner of one it's the strangest thing you'll find in ecrap)
Without the flashing the bare board is of no value at all and tend to be recycled into play equipment and park benches... if the end recycler recycles them at all.

The small board will likely be low grade for boardsort.
The large one is probably going to be peripheral but depending on thickness may go as high as telco.

That said looks like the work of the Ru factory in Taiwan that Motorola used for nearly 3 decades and my guess is closer to peripheral class for tge big one at $1-$1.50/lb value.