Howdy!
Hapkido footwork is far more linear than Aikido footwork in my experience. We move on the "X" like Aikido but from there even our circular motion tends to be more 'abrupt' and generally speaking, we use smaller, downward circles (spirals?). This is easiest to observe if you watch Sin Moo HKD style joint locking next to similar locking techniques from Aikido.
Another good example would be the movement called 'tenkan' in Aikido - while we will use a circular motion, our circle tends to resemble a corkscrew more than a true circle. For the most part, we will tend to 'bring them in' instead of projecting them away. And we will then "finish" them on the ground.
A couple of generalizations but I think it gives you the "flavor" of what I'm trying to convey. Maybe some folks with more experience can put it into words better than I can...?
As for stances, because we also kick and punch, we tend to use 'fighting stances' more like those of some of the striking arts (i.e.; Boxing) when we are not just standing 'naturally' or adopting a 'submissive' body posture. We have horse stances & front stances, but these are positions we will move "into and through" as opposed to starting or finishing with those movements.
Of course every teacher is different. We tend to focus on drilling footwork more than anything else because it has to become muscle memory or it's useless. For example, what good is it to know 100 different joint locks if you get knocked the ____ out while you are trying to "enter" on your opponent?!?So for us, the footwork associated with entering & standing control of the opponent (whether he's trying to strike or grapple with you) is of paramount importance.
Against a resisting, trained opponent (versus a trained but cooperative partner), a slightly more linear and agressive approach is necessary. At least IMO. However, find an agressive, pre-war style Aikido player and his footwork will probably resemble ours a bit more than most.
Just my take on it. Hopefully you will get some more input from some others...