The primary difference is the strength of the acid. Acidic strength is measured in pH, which measures the number of H+ ions in a solution. Sulfuric acid, for example, is H₂SO₄, but in solution will go to 2H+ +SO₄(2-). It is largely the reactions of these corrosive ions with your skin that burns. Weaker acids are less likely to dissociate and release H+ ions. Note, however, that bases which have OH- ions free in solution, will also burn your skin. An acid and a base will neutralize each other, though.

It's not so much that acids are harmful or not harmful, but that acids have varying strengths.

An acid is any compound that when dissolved in water can dissociate and release a hydrogen ion (basically a proton). Water itself is an acid, although a very weak one (it's just as powerful a base, the opposite of an acid, as it is an acid). More powerful acids have a higher proportion of their molecules that will release the proton. The concentration of protons in a solution changes the pH, or acidity, of that solution, which in turn changes the way it interacts with other things which it comes in contact with. Extremely low pH solutions tend to burn things, as do extremely high pH solutions. Making a solution mildly acid can be accomplished by either adding a lot of a weak acid, or a very small amount of a strong one.Now, for the acids in foods, remember what the acid is: it's a molecule that can give off a proton. In most cases, however, in foods we are interested in the anion, the negatively charged molecule left behind when the proton leaves, rather than in the fact that it is an acid and gives off a proton itself. Ascorbic acid (vitamin C) is an example of this: we want the carbon-based compound, and don't really care that it's an acid. Hydrochloric (HCl) acid is good in small amounts, because we need the chlorine, but ordinarily we get the chlorine from another source, namely sodium chloride (table salt).