Do these go as integrated motherboards or high peripheral?

Those are without a doubt Laptop Boards. I would submit them to Boardsort in the Laptop Category.
Here to learn like everybody else.

They def came from laptops but they aren’t socketed processors so doesn’t that put them in the integrated motherboard category?

This might have changed, but previously if it was the mainboard out of a laptop, it went as a laptop mobo even if the CPU was soldered/no socket.

The green board has a GOLD Tab BGA chip on it. If you look at the Integrated Motherboard category. It makes a note. NO BGA. That upgrades that green board. I still think Laptop Motherboard.
Also. For now. Clean that heatsink paste off the one chip on the blue board. I want to look it up. Also remove the shield in the corner. Should be chips under the shield. Then. Please repost the blue board.
As a sidenote. You could email Chris about those 2 boards also. I can't wait till O.S.C.A.R. comes back.
Here to learn like everybody else.

The shield on the blue appears to be an integrated wifi card, so definitely cos under that.

Anything on the other side of either board?

I concur with what's been said already, generally laptop boards will stay as laptop. As things get miniaturized more and more and it takes less valuable material to build computers, the value of scrap will definitely change. The Dell board looks a little older/better materials compared to the blue one, which may be new enough to be less valuable. But does it dip out of laptop grade..? ¯\_(ツ)_/¯

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Here to learn more so I can recycle more
My grades are my own opinion and not an official grade from Boardsort