Why do some recipes call for 1 Tablespoon of vinegar & some call for only 1 teaspoon of vinegar??  What is it that the vinegar does to the batter?  why such a difference?  Any help would be great.

ASince vegan cakes do not have eggs, the combination of vinegar and baking soda or baking powder helps with leavening and reduces the density of the cake. If the recipe normally uses more eggs it would require more vinegar (and baking soda/powder) to compensate.

Same principle as the baking soda volcano you often see at science fairs.