Sneezing is to clear the uppermost portion of the airways (the
nasopharynx) while coughing is for the lower airways. If a
particulate is trapped in the lower airways, we don't need to take
in more air (as this if it happens, which is impossible, this will
dislodge the particulate and makes it travel even deeper into the
lowermost portion of the airways), hence coughing, which does not
involve a series of inspiration, sometimes, only one is enough to
generate enough energy or momentum (the distance from the
particulate to the mouth is further) to bring out the irritant.
Given this fact, you should be able to think out why sneezing
requires a series of inspiratory effort.
Both are served by different cranial nerves from the brain.
