What is the cause of "alcohol burn" in beverages?

Alcohol is a very good solvent, so can and does contain chemicals and stuff in solution. The brown ones would seem to contain different substances then the clear, and as suggested stuff from the barrel wood that the were aged in.

Another possible factor, since it’s just not alcohol, but mostly a mixture of water + alcohol (and dissolved chemicals.) As the drink becomes more diluted it is possible for some of those items that are dissolved to come out of solution which might cause a burn when the drink mixes with the moisture in the mouth and throat. One drink in particular, absinth, uses this effect of stuff come out of solution due to dilution as part of it’s normal way of consuming it.