Of course all this depends upon the jurisdiction in which the offense occurs, in some venues they are truly synonymous - in others the specific predicates are (slightly) different. The most common (and commonly known) element of blackmail is the threat of releasing derogatory information but GUW is right, in many jurisdictions it is not the only one.

The IMPORTANT thing is that only in the most exceptionally rare circumstances are government employees held criminally liable for coercion. Coercion is a time-honored and tested tool in the law enforcement/prosecutorial toolkit - the most that ever happens is the evidence resulting from an illegal search are excluded at trial and the government's case falls apart. Possibly the bad actor might suffer some kind of adverse personnel action (such as a letter of reprimand, or a poor annual evaluation) that maybe stalls career advancement, but who knows....?

Small consolation for the aggrieved citizen(s)......