Denatured alcohol is 90% ethanol (the alcohol in booz) which has an addtive to render it otherwise undrinkable. Traditionally, the main additive was 10% methanol, which gave rise to its name, but this is not always the case now.
In the phrase denatured alcohol, denatured means "a specific property of ethanol, its usefulness as a beverage, is removed". The ethanol molecule is not denatured in the sense that its chemical structure is altered. The liquid is only toxic if you either drink it or perhaps bath in it. You do not need gloves to handle it, like when you imbibe Blue Coolade. It is not the methanol itself that is toxic, but the accumulation of metabolites of the methanol in the body.