I'm sure there is some carryover, but they also feel very different.
When I'm doing shoulder cleans there is perhaps a bit more squat and pull from the back, a little less glute - though the mechanics are maybe increasingly similar as the swing weight increases.
I also cannot be sure, but I'd say the shoulder cleans maybe are more explosive (?) as I normally come bodily off the floor when the bag comes up - it is ballistic by the time it reaches my sternum and my heel if not my entire foot is airborne as well. This with a 60-70lb bag for reps, the same as my normal load for reps with the Swing, but where (at a guess) I could hit around 40 2-hand swings AMRAP with that weight, I'm not at all confident I could get half as many with a comparable sandbag.
In common they both initiate from a hips-back hinge and require attentive shoulder packing under tension.
Not in common the shoulder clean does not have a rhythm and backswing component. I set (not drop) the bag down after every rep, push hips back, pack the shoulders and go - there is a half-beat when I reset no matter how fast I'm going. Also not in common you have to get that little bit lower to initiate as you're scraping the bag off the floor and need to get your hands under it.
They definitely have more in common than not. As the bag weight goes up they will have less in common though - done with a 90 or 100lb bag, I'm not exploding anywhere. Every hoist is a round back heft, hips drop, and then I go up - crossing over more to a push press of sorts, an over/under Zircher-hold launch to shoulder from a squat.
Edit to add: you can also bearhug the heavier bag in a bent over posture and use fairly pure hinge motion to launch it up, but still the similarities to a swing are less as the bag weight increases.