Another underappreciated distinction is between "essential" and "frontline" workers, with frontline defined as people who can't perform their jobs from home. The case for frontline workers getting vaccine priority >> essential but not frontline.
https://www.nytimes.com/2020/12/05/health/covid-vaccine-first.html

Frontline also sets up a more objective test. Have you been required to work on site for the past 9 months? If so, maybe you'd get priority for vaccines. If not, you wouldn't. (If the answer is "sometimes", maybe you're in tier 2a or whatever.)

But the job categories in gray on this chart—jobs that are "essential" but *not* frontline—tend to be in politically powerful industries. So when guidelines refer to essential rather than frontline/on-site work, they may be a reflection of that power.