The māʻitaki (a word related to the Samoan tamataʻi (lady)) was a daughter of the Tuʻi Haʻatakalaua who married with the Tuʻi Tonga to become his principal wife and the mother of his heir.
As personal rank in Tonga comes from the mother, this elevated the status of the future Tuʻi Tongas, and increased the power of the Tuʻi Haʻatakalauas, because of the fahu system.
Originally, however, the term was to indicate a young woman sleeping with a visiting chief, as was normal in former times.
(Tongotea's older sister Halaevalu also married a Tuʻi Tonga, but this seems to have been more a try out, and she did not become mother of the next king).
As consequence nowadays the word māʻitaki has degenerated into a general term for concubine, while moheofo is a reference to the royal family.