Are the AIIR Watch Purifier and the AIIR Watch Negative Pressure Machine the same unit?

Yes, the unit itself is the same. 

The purifier is a stand-alone unit that recirculates purified air. 

The negative pressure machine creates a negative pressure in a space and is the only way to improve the effectiveness of an isolation space. The negative pressure machine includes exhaust accessories to exhaust the air out of the space, that air removal is what creates the negative pressure. The air that is exhausted out is purified using the same method as the purifier units, because it is the same unit. The negative pressure machine (AA and NA options) also includes a Setra LITE Room Pressure Monitor which can be mounted outside the isolation space to continuously monitor the status of the negative pressure in the space.