I suppose there's some personal judgement involved, but I would disagree that the main difference is just at the point of contact. If I hooked up two long wires to the probes of a stun gun and clipped them to someone, I would still say that the Taser is delivering a different type of discharge.

Stun guns are very high voltage (I see 1 million volt models advertised), low amperage, DC devices. Usually only a handful of mA of current, which your typical 9V battery can support.

From this article:
Introduction of the Taser into British policing. Implications for UK emergency departments: an overview of electronic weaponry. Emerg Med J 2004;21:136–140

The authors state, "The Advanced Taser delivers a sequence of half sine wave current pulses, each having a peak amplitude of about 18 amps and a duration of about 11 microseconds. The peak voltage output of the device is as high as 50 000 volts." Still DC, but now rapidly pulsing, unlike the constant DC discharge of a stun gun. Tasers don't use as high a voltage as many/most stun guns but are higher powered, requiring a brick of AA batteries or a lithium ion battery pack, as in the new C2 model. The authors don't mention whether the pulsing characterstics are constant or change, so it's possible that the Taser unit adjusts the discharge as well, but that's just conjecture on my part. For example, perhaps the peak amplitude is highest at the start of the discharge, but gradually tapers because the subject's muscles will be quite fatigued by then, particularly at the end of a 30-second long C2 discharge. I only mention this possibility because of some foggy recollection of something I read a long time ago regarding the Taser, but maybe it was just marketing BS.

The authors further explain that it is thought that the high frequency pulsing helps protect the subject of a Taser strike from cardiac disturbances from the discharge because high frequency discharges will tend to remain on the surface of the conductor, in this case, the skin. Like a Faraday cage effect. This helps protect the heart and other internal organs from the brunt of the discharge, particularly the longer shock times (30 seconds) of the C2 model, and would theoretically seem to help distribute the charge to even more muscles and nerves near the skin than a simple DC current would propogate. (my opinions, not the authors')

Is this really different or just a tweak of the same thing? Well, that's in the eye of the beholder, I suppose. But to me, a stun gun does not work the same as a Taser, although Tasers are an evolution of the original stun guns, so of course, there is a great deal they have in common.