"My mom is a pensioner."
Translation:Моя мама - пенсіонерка.
Does this mean literally someone who receives a pension, to be said in the context of some job, contrasting with those who are not yet retired, as in the U.S.; or does it simply mean any older person, who is eligible perhaps for some government old-age programme, as in (as I understand it) the UK?
Yes, usually this means "literally someone who receives a pension, to be said in the context of some job". Here in Ukraine more or less all the people can have some pension after retire despite that is could very small funds.