I'm assuming that by 'fundamentally different' you mean something which is naturally a positive liberty in your view, represented (presumably disingenuously in your opinion) as a negative liberty. I don't see how this distinction can be made however.

No, you're not getting the difference between positive and negative -- possibly I'm doing a poor job of explaining. Let me try one more time, and include a reference for further explanation.

A negative liberty is enjoyed when I'm free of external limitations. I am allowed to do whatever I am able. The Bill of Rights is full of this stuff: free speech, freedom from seizure of property; etc.

A positive liberty is enjoyed when someone empowers me to be able to do something. The health care debate hinges on the idea that society (by way of the gov't) must give healthcare to all who need it. You'll note here the critical element of an external agent providing the positive liberty.

If I'm alone on a desert island, I have infinite negative liberty. However, positive liberties are quite impossible since there's no agent to enable me.

For further discussion, see this Wikipedia article:
https://secure.wikimedia.org/wikipedia/en/wiki/Liberty

Individualist and classical liberal conceptions of liberty relate to the freedom of the individual from outside compulsion or coercion and this is defined as negative liberty. Social liberal conceptions of liberty relate freedom to social structure and agency and this is defined as positive liberty.

The slavery example is not a counter-argument. The fact that someone who had been using you unjustly is now forced to mend his ways does not force us to look at something as a positive liberty -- else everything would be. Two centuries ago there were a lot of people doing something very evil. Damaging their livelihood by recognizing their victim's rights was only the transient consequence of righting the wrong, and is of no significance today. I have no obligation placed on me by the recognition that all my fellow humans own their own bodies. That is the crucial distinction.

The fact that an external agent -- the other people in society -- must provide your positive liberty creates the odd condition in the healthcare question. Abstractly, I'm entitled to some healthcare, but the amount to which I'm entitled is fundamentally variable because the resources available to provide it are variable. One can imagine that I'm in the middle of a cancer treatment that I'd been "entitled to" when the stock market crashes and gov't tax revenue falls dramatically. With less money in the budget, the thresholds for what care can be provided must be shifted, and now I'm told that I'm no longer entitled to that expensive treatment. I have trouble accepting a moral code in which the difference between right and wrong (what we are morally obligated to provide to someone, in this case) can change with the business cycle and even with fashion.

As an aside, the question of slavery is an extreme example here, but there is a conjunction. In the presence of positive liberty, the person claiming the liberty is indirectly claiming ownership of me (in a small degree). They assert that I must work in order to earn the resources that will enable their liberty (that is, I must pay into a fund so that they can get healthcare). In this way, positive liberties are directly destrictive of negative liberties.