The mini-14 is an M-14 action shrunk down for intermediate cartridges.
M1 Garand, M1 Carbine, M-14, Mini-14/30, and current Deerfield are all very similar gas-operated designs, with a long, relatively heavy gas piston with a long operating rod running along the side of the barrel and receiver, with the slide handle on the end of it. This mechanism operates a rotating bolt that locks much like a bolt action. The track and lugs that rotate the bolt, the way the bolt is inserted into the receiver, etc., in Ruger's Minis, all of it was taken from the M1 family design.
That doesn't mean they share parts, but if you've ever cleaned a Mini-14, you'll note that the design, conceptually, was practically lifted straight from the M1 family, just like the bolt lifts out of the receiver.
This is the receiver of an M1 Carbine, which looks familiar to shooters of any of the abovementioned Rugers and USGI guns, even if they've never seen an M1 Carbine:
Contrast that with this picture of the SKS, clearly a VERY different design:
Here is an M14:
and a Garand:
This AK47 has some similarity with the SKS, but none with the M1, M1 Carbine, M14, Mini or Deerfield:
So clearly, the M1 Carbine, which was in Bill Ruger's mind when designing the look and feel, but not the action, of the 10/22, has a very close relationship to the actual design of Ruger's gas-operated guns.