Is clear vanilla extract the same as brown vanilla extract?

No, they are not the same. Clear vanilla extract is made with glycerine and predominately used by fondant cake makers or for icings that are needed to remain absolutely white. They're are some people who buy it because its label reads "NO ALCOHOL", even though it is still made with an alcohol solvent. The end result still contains a minute amount, but not enough for the FDA to have it listed as an ingredient.