The basic distinction is how the yeast is intended to be used, given the processing techniques of the producer. Active dry is intended to be added to wet ingredients. Instant yeast is intended to be added to dry ingredients.
Instant yeast is a great boon for a professional bakery since the time (and labor) required to dissolve yeast is eliminated and we all know that "time is money". It is a convenience for the home baker.
If bakers always did things according to other's intentions, that would be the end of the story. Before we go there, here is a bit of info on "intentions" culled from rec.food.baking
|Active dry yeast is a yeast which is developed to be dissolved prior to use. It will work without dissolving but if you were doing laboratory tests with all variables tightly controlled you would see that for optimum yeast activity and gas production, this yeast does best when dissolved in some water (About 1/4 cup per package - or 2 1/4 teaspoons - is a good amount to use.)...
With instant types of yeast optimum gas production is achieved when the yeast is mixed into the dough with the flour as part of the dry ingredients. However, instant yeasts can also be dissolved but again if you were doing laboratory tests you would find that best results, as far as gas production goes, are achieved by mixing the yeast in as a dry ingredient. When instant yeasts are dissolved, the water has the potential to damage the yeast cell due to osmotic pressure.
Obsessed home bakers are notorious for breaking the rules - rec.food.baking has threads where bakers report adding AD to dry ingredients, Instant to wet ingredients with no adverse results. The bias, however, is to report successes, not failures.
Dissolving a solid in a liquid is exactly what it says. Does the temperature of the liquid matter when dissolving Active Dry yeast? Sure - yeast cells begin to die off at a temp of about 130F and even the most robust yeast cells will die at 140F. "Warm" (90-125F) water probably helps the yeast dissolve slightly more quickly - cool (75-90F) water will do the trick, it will simply take a few minutes longer. Yeast cells become dormant at 40F (dormant does not mean dead, just deactivated).
Dissolving is not proofing.
Proofing is exactly what it says; you're looking for "proof" that the yeast can multiply. Adequate "proof" is visible bubbles (a by-product of yeast multiplication) or a "yeasty" smell or froth at the top of the liquid or some other criterion easily accessible to humans without microscopes To proof yeast, you dissolve it and give it some food - a little sugar and/or flour added to the water is most common because they're so convenient.
If you just dissolve yeast in water but don't give it some food you're not "proofing" it. You don't know whether the yeast is dead or alive or how robust (on the average) all those zillions of yeast cells actually are. On the other hand, companies that sell AD yeast would go out of business pretty quickly if their product didn't work or needed expensive storage conditions to survive. The commercial manufacture and sale of AD yeast started around 1870 (in the US) so they've had lots of practice.