mask or respirator, the difference between them?

Refer to the definition on Wikipedia, A mask is an object normally worn on the face, typically for protection, disguise, performance, or entertainment. Here, we are talking about the personal protection mask.
On the other hand, refer to the definition on Wikipedia,  a respirator is a device designed to protect the wearer from inhaling hazardous atmospheres, including fumes, vapors, gases, and particulate matter such as dust and airborne microorganisms. There are two main categories: the air-purifying respirator, in which respirable air is obtained by filtering a contaminated atmosphere, and the air-supplied respirator, in which an alternate supply of breathable air is delivered.
So the main difference between mask and respirator is if it can stop inhaling hazardous atmospheres or not. Obviously, the personal protective mask can not stop inhaling hazardous atmospheres, because it does not have a good seal around the edge between the mask body and face.
Here is a table shows you an alternative for mask/respirator in the U.S.A. and Europe.