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on most MBs, there are 2 heatsinks, the big one is for the CPU. What is the chip under the smaller one. What does it get sorted as??

Never remove soldered chips from a motherboard. The motherboard instantly drops to midgrade.
That said there are boards that have non-CPU chips in sockets.
First for grading: in modern times these will almost always be LGA chips in a metal or plastic compression socket. LGA, land grid array, chips are pinless.
On occasion and with older equipment (mid/2000s back) you find PGA, pin, chips. These go as green fibre with or without metal.

As to what it is, it depends on the age of the board. Generally the CPU and Bridge chips have heatsinks. Bridge chips are literally bridges between various controllers and the cpu. They send data around. Bridge chips (north, south, gateway, express, etc) are multiple controllers on a single chip.
In the old days there were dozens, hundreds, of tiny little chips. As transistor size decreased, and chips produced less heat, they started combining controllers into bridge chips. Math and acceleration units like the i387 and i487 were merged into the CPU with the Pentium/586 era.
3D acceleration moved into the GPU itself. Shortly after that.
Component Memory, timers, syncs, and controllers etc moved into the bridge chips.

Today even the bridge chip is near extinction. For x86 and AMD64 (aka 86-64 and x64) a single I/o chip and a single A-ASIC (all-in-one application specific integrated circuit/controller) has taken the place of the bridge chips in most systems from phones to servers. Some of the AMD A series APUs do away with the methodology entirely. Using a single ASIC and the Ryzen APU.
Even this is at an end with ARM now. Google and Apple are both working on, and have, respectively, ARM APUs that do away with memory controllers as the controller and system ram are now part of the CPU/APU itself.

Eventually motherboards will be the size of a old small flip phone with dozens of fat wires to plug everything in. Nothing but a big fat chip and wire ports.

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I sell the motherboards to a local yard for 1.20lb, I usually pull the gold corner BGA off because I get the same price with or without it. So I got to thinking about that other chip under the smaller heatsink as was kind of hoping that it would go as a GC BGA due to the gold on the corners of it if not, what would BS buy them as? Thanks for the info on what it does, pretty interesting.

Yes they’re BGA (flat packs), with or without tabs/corner

Here a short visual history.

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