Everything under FCC part 15 subpart B is an unintentional emitter (intentional emitters are covered under FCC part 15 subpart C). Scanners and radar detectors are two examples of part 15-B unitentional emitters that do
require certification and thus an FCC ID.
Class A and class B have differing radiation and conduction limits, the definition is based on industrial or residential use not on emissions.
From FCC part 15.3:
(h) Class A digital device. A digital device that is marketed for use in a commercial, industrial or business environment, exclusive of a device which is marketed for use by the general public or is intended to be used in the home.Disclaimer: I haven't passed the bar since my last post, so I am still not a lawyer.
(i) Class B digital device. A digital device that is marketed for use in a residential environment notwithstanding use in commercial, business and industrial environments. Examples of such devices include, but are not limited to, personal computers, calculators, and similar electronic devices that are marketed for use by the general public.