Inside the chair (built-in)

("Hidden" under the chair's base plate cover, joined to the air/waste/water plumbing in the floor under/in front of the chair)

Images are from the Anya-A2000 Dental Chair. 

Outside the chair (external)

(As a separate unit in a box usually positioned next to the spittoon/cuspidor side box. This is joined to the air/waste/water plumbing on floor on the side of the chair instead of "under" the chair. )

Images are from the Anya-A2000 Dental Chair.

Observe how the box can't be placed right under the spittoon due to lack of space and will therefore need to be placed slightly to the side.