Is bunker sand and topdressing sand the same?

You can use the same sand for both but they are not the same.  Topdressing sand is designed more for the purpose of topdressing turf and the gradation is composed of medium sized particles.  The same sand is not optimal for bunkers as it can become unstable and lead to fried egg lies or buried balls (low penetrometer readings).  However, your bunker sand should not contain particles that if hit onto the green cause damage (large particles).  Bunker sand is designed with more uniform gradation and angular particle shapes.