Face mask, any:
"Face masks" can be any mask on a face, including home made masks.
These include many masks you see people wearing on the street, usually from a wide variety of manufacturers, street vendors, and shops.
Surgical mask:
"Surgical masks" are distributed to hospitals and consumers as a professionally manufactured, mass produced mask, normally made from nonwoven polypropylene conforming to certain specifications. They are intended to be single use, throw away masks, but they can be disinfected, cleaned, and reused at times of shortage such as during a pandemic.
Respirator, disposable:
Respirator, reusable:
"Respirators" are masks which are sealed against the face for no inward air leakage. They should have firm but bendable materials so they can be bent to conform to the face and maintain their shape while in use, they should have tight straps, and they should be carefully fitted to the face and checked carefully.
The one on the above left is a one piece, disposable respirator. They often are not very bendable, and depend a lot on just tight straps.
Note the metal nose clip. These are supposed to make the respirator seal better around the nose, but on many masks they don't work so well and may not be comfortable. If they don't seal, then they're really a face mask, not a respirator, so be careful about claims.
Other respirators come as reusable, whereby the filters inside are replaceable. They typically seal the face by a soft material and/or by being bendable to some extent without deforming back too much under tight straps.
