Three numbers that sound alike and mean different things.
Reach is how many separate people saw the post.
Impressions is how many times it was shown. One person scrolling past it three times is one reach and three impressions, which is why impressions is always the larger number and the more flattering one.
Engagement is how many people did something — liked, commented, shared, clicked.
Which one matters
Engagement, and it is not close. Reach and impressions measure distribution, which the platform controls. Engagement measures whether anyone cared, which is the only part you influence.
Engagement rate — engagement divided by reach — is the honest version, because it does not reward a post that was simply shown to more people.
For a service business specifically
None of these are customers. A post with excellent engagement and no phone call has not done its job. The metric that matters most is the one social platforms cannot report: whether anyone got in touch.
Treat engagement as a signal that the content is landing, and the phone as the measure of whether it works.