I get the feeling that walking lunges are better for balance, but other than that - especially in terms of muscles used and caloric burn - are there any significant differences?
I'll assume you're talking about lunge variants close to these:
The walking lunge starts with the first part of the forward lunge (getting down into the lunge), and ends with the second part of the backward lunge (coming back up out of the lunge).
While doing walking lunges, you never get the second part of the forward lunge (coming back out of the lunge by pushing back to your starting position).
While doing walking lunges, you never get the first part of the rearward lunge (stepping back from your starting position into a lunge).
These differences are not significant with respect to muscles used, calories burned, or balance improvement.