A CRM, AMS and UMS can all store people and communication data. The meaningful difference is the model around those records and the procedures the software can support without forcing a union to rebuild its work from generic components.
A union may need constituent communication, membership administration, dues-related information, locals and bargaining units, positions and terms, agreements and articles, grievances, representation assignments, meetings, documents, authenticated member experiences and public websites. No acronym guarantees all of those capabilities.
Use the categories below to form hypotheses, then require vendors to demonstrate the specific workflows your organization needs.