which of these do they mean?
* The Classical Greek trio[citation needed] of Zeus (father), Leto (mother), and Apollo (son)
* In ancient Egypt there were many triads, the most famous among them that of Osiris (man), Isis (wife), and Horus (son), local triads like the Theban triad of Amun, Mut and Khonsu and the Memphite triad of Ptah, Sekhmet and Nefertem, the sungod Ra, whose form in the morning was Kheper, at noon Re-Horakhty and in the evening Atum, and many others.[34]
* The Roman Capitoline Triad of Jupiter (father), Juno (wife), and Minerva (daughter).
* The Roman triad of Ceres, Liber Pater and Libera (or its Greek counterpart with Demeter, Dionysos and Kore)
* The Julian triads of the early Roman Principate:
o Venus Genetrix, Divus Iulius, and Clementia Caesaris
o Divus Iulius, Divi filius and Genius Augusti
o Eastern variants of the Julian triad, e.g. in Asia Minor: Dea Roma, Divus Iulius and Genius Augusti (or Divi filius)
* The Matres (Deae Matres/Dea Matrona) in Roman mythology
* The Fates or Furies in Greek and Roman mythology
* The Hooded Spirits or Genii Cucullati
* The sisters Uksáhkká, Juksáhkká and Sáhráhkká in Sámi mythology.
* The triad of Al-Lat, Al-Uzza, and Manat in the time of Mohammed (surah 53:19-22)
* Lugus (Esus, Toutatis and Taranis) in Celtic mythology
* Odin, Vili and Ve in Germanic mythology
* The Norns in Germanic mythology
* The Triglav in Slavic mythology
* The Trinity in Christianity
* The One, the Thought (or Intellect) and the Soul in Neoplatonism
* The Saha Realm Trinity in Mahayana Buddhism (Shakyamuni, Avalokitesvara and Ksitigarbha)
* Brahma, Vishnu, and Shiva (Trimurti) in Hindu mythology
* Shakti, Lakshmi, and Saraswati (Tridevi) in Hindu mythology
* The Three Pure Ones in Taoism
* The Fu Lu Shou in Taoism
* Ayyavazhi Trinity
* The Triple Goddess in Wicca
* Nuit, Hadit and Ra Hoor Khuit in the Thelemic spiritual system
(source: http://en.wikipedia.org/wiki/Triple_deities)
As you’ve noted in your question, it depends on who you ask. I have had friends who practiced Paganism, and when they spoke of a trinity people often took it for granted that they had Christianity’s Trinitarian concept in mind. This, as you can imagine, caused great confusion and showed a lack of respect for my friend’s personal convictions.
If one cannot tell on the basis on the conversation’s context, one should ask. Even when one explains which of these you listed they are speaking of, we should also not take it for granted that we know precisely what they are talking of if we do not share their belief. So we should ask them to explain their understanding of what they are speaking of.
The world is filled with enough confusion, bias, prejudice, and the like that we should avoid trying to find fault with the belief system or lack thereof that another person holds to. Especially should we be mindful to ask if we need clarification, which hopefully we will do without adding our own misunderstanding to further any gaps in humanity that need to be mended.