From "Okrand's Notes," HolQeD 4:4 p. 11.

"An organization dedicated to scholastic pursuits or research is a yejHaD 'institute' or 'institution' or a yej'an 'society.' The distinction between yejHaD and yej'an is not clear, though the former is usually -- but not always -- used for larger organizations. It is not known whether the first syllable of these words (yej) is yej 'council, assembly,' but there could be some historic connection.

Note that nugh 'society' has a much broader meaning: a group of people with a shared culture. Accordingly, tlhIngan nugh would mean "Klingon society" as distinguished from, say, Romulan society, but tlhIngan yej'an would probably be 'the Klingon Society,' a group dedicated to the study of Klingons."

nugh is used when referring to a group with a shared culture (common beliefs, values, traditions, knowledge, etc.) and (usually) shared territory whose members interact with each other in accordance with shared norms.

yej'an is an intentionally formed organization of people and is not infrequently used in the name of that organization. (In this usage, it could be translated "society," but also "organization, association, guild" and many other things.)

For "community," meaning a group of people with a shared (and probably relatively narrow) interest or common defining characteristic, such as the "Klingon-speaking community," use the term yuvwan. A yuvwan is generally not a formally or officially organized group.