Right, the mobility looks different though - you don't move unless it's NECESSARY, while boxing involves varying degrees of dancing around. At least in the ring. I think the one thing I like better about WC's version of 'mobility' is that if you stay focused, you cannot be faked out. Think of it like this - A WC fighter is in standard WC guard (Wu Sao, Man sao, square stance) facing off with a boxer who skips around and circles, looking for a way in. Eventually, someone is going to have to hit first. If it's the boxer, he may try to set up a combo by using a feint of some sort, but the WC guy - if he's good - will deflect the feint and attack the same way as if it were an outright jab/cross. If the boxer's guard goes up it is moved, continue attack. If he counter attacks, the WC guy uses his hand boxing techniques as quickly and instinctively as needed and continues attack. Attacks should of course not be just 'chanin punching' (which i really don't believe in at all), but a totally invasive, adaptive assault that utterly destroys the opponent's structure, thus destroying them. Boxers on the other hand may over-strategize, spending too much time resetting and trying different tactics to get in.
Hopefully, this type of fighting does not commence in SD situations, but style can certainly be an entrapment.