I've thought through the "all tires rotate at the same speed" thing before and how it works mechanically (front differential, rear differential, transfer case) and I think in the "no differentials locked" condition the correct statement is: the sum of the front wheel speeds == the sum of the rear wheel speeds. So you can have your front wheels slip and the rear wheels can still get power, or you can have your rear wheels slip and the front wheels still get power, but if you have one wheel in the front and one wheel in the back that are slipping, you're hosed.

Re: the 3 locking mechanisms comment, in typical 4WD configurations the transfer case in 4H/4L is essentially locked (which is what makes the above sum front == sum rear condition). AWD transfer cases can be more flexible there; some essentially act as a 3rd differential and result in all four wheel speeds being essentially decoupled (for better or worse, easier to get stuck) while others actively control the front/back locking with clutches or hydraulics or whatever.