What's the relationship between docker and runc?

Docker starts containers in /run/docker/runtime-runc/moby/ and /run/docker/runtime-runc/plugins.moby/. You can see them with runc by using --root option:

~# runc --root /run/docker/runtime-runc/moby/ listID                                                                 PID         STATUS      BUNDLE                                                                                                                CREATED                          OWNER4a81e5e9babc18e2bd7eaf560a9d0ab1bff7fb9145acacd9445d313f2b40f3ef   4159        running     /run/containerd/io.containerd.runtime.v2.task/moby/4a81e5e9babc18e2bd7eaf560a9d0ab1bff7fb9145acacd9445d313f2b40f3ef   2021-05-14T06:26:25.894963575Z   root9e88f71c7f4814d87252b2defcb22aa5c851511d8ed27dd1b4d260a116358090   5072        running     /run/containerd/io.containerd.runtime.v2.task/moby/9e88f71c7f4814d87252b2defcb22aa5c851511d8ed27dd1b4d260a116358090   2021-05-14T06:26:34.330942248Z   rootaba4e2c0534a0d79bafa19a81aa412eb61848451ebfa1122af58197d3c8a8f39   4169        running     /run/containerd/io.containerd.runtime.v2.task/moby/aba4e2c0534a0d79bafa19a81aa412eb61848451ebfa1122af58197d3c8a8f39   2021-05-14T06:26:26.09091234Z    rootbc9377f463e7dc47bd58d80a62b0ba4da6fc86869f40d41dc181b7c9f057b2f5   4199        running     /run/containerd/io.containerd.runtime.v2.task/moby/bc9377f463e7dc47bd58d80a62b0ba4da6fc86869f40d41dc181b7c9f057b2f5   2021-05-14T06:26:26.090912342Z   roote554c565e3c270d4630f91ec8ab5e97379720ab950f1c9f285e31b95929e46dc   5071        running     /run/containerd/io.containerd.runtime.v2.task/moby/e554c565e3c270d4630f91ec8ab5e97379720ab950f1c9f285e31b95929e46dc   2021-05-14T06:26:34.299062098Z   rootef49f937f358db1debec1037796972f00a6a030c15f2b471053b81d01f1b6bb5   4952        running     /run/containerd/io.containerd.runtime.v2.task/moby/ef49f937f358db1debec1037796972f00a6a030c15f2b471053b81d01f1b6bb5   2021-05-14T06:26:33.927094868Z   root

As for the relationship, it has been answered here.