inverse agonist
Some receptors hum along at a low level even with no signal present — like an engine idling. An inverse agonist is a drug that turns that idle down, pushing the receptor below its resting, baseline activity rather than merely stopping a signal.
This is only meaningful for receptors that have constitutive (spontaneous) activity. A plain antagonist would just hold that idle steady by blocking other ligands, but an inverse agonist actively stabilises the receptor in its inactive shape, reducing signalling below baseline. It therefore has negative efficacy, in contrast to an agonist's positive efficacy and an antagonist's zero efficacy.
Many drugs once labelled antagonists are now recognised as inverse agonists at receptors with measurable constitutive activity. Some antihistamines and certain beta-blockers fall into this category. In practice the distinction matters most where basal receptor tone contributes to a disease, though for many clinical purposes inverse agonists and antagonists behave similarly.
The antihistamine cetirizine acts as an inverse agonist at the H1 receptor, shifting receptors toward the inactive state and lowering background histamine signalling.
Driving activity below baseline.
Without constitutive receptor activity there is nothing to suppress, so an inverse agonist and a neutral antagonist become indistinguishable in that setting.