The ground itself, not what gets added to it
Subgrade is not a product that shows up on a delivery ticket. It is the soil that was already on your lot, cut and graded to the shape the job needs and compacted where it sits. Subbase is the separate layer of crushed stone that goes on top of it. Confusing the two matters because they get fixed differently: bad subgrade means dealing with the actual dirt, moving it, draining it or compacting it in place, while a thin or poorly compacted subbase is a matter of adding or reworking the stone above it.
Why clay changes what the ground needs
A lot of the ground around here is red clay, and clay behaves differently than sandy or gravelly soil. It holds water instead of shedding it, and it swells and shrinks as it wets and dries through the seasons. Subgrade on a clay site gets graded to shed water away from the pour instead of letting it pond, and gets compacted enough that it will not keep moving once stone and concrete are sitting on top of it. Sandier ground still needs grading and compaction, it just does not carry the same swelling risk.
What bad subgrade does to a slab later
Concrete is strong under a load pressing straight down and weak when it is asked to bridge a gap. If the subgrade underneath settles, washes out, or was never compacted to begin with, it leaves the slab spanning a void it was never built to span. That shows up months or years later as a cracked corner, a section that has dropped relative to the rest of the pour, or a joint that has opened wider than the rest. Most of what looks like a concrete failure traces back to what the ground was doing underneath it.