Psionics/Psion is a modern term, coined in 1956, by John W. Campbell Jr. for the February issue of his Astounding Science Fiction magazine. It was an expansion of an earlier term, psi, coined by the science fiction authors B.P. Wiesner and Robert H. Thouless in 1942.
Psychic is a slightly older term, though still relatively modern, coined by French astronomer and spiritualist Camille Flammarion in the mid-1800’s, and later introduced to the English language by publisher Edward William Cox in the 1870’s.
Earlier archaic terms for such abilities, as opposed to the concept of Magic in western culture, are found in Indian Hindu and Buddhist beliefs. In Hindu and Tibetan/Chinese Bhudism the practice is called Sādhanā, in Japanese Bhudism it’s called Shugendo. Practitioners in Hindu are called Siddhas, in Japanese Buddhism they are called Shugenja (yet another thing D&D got wrong…). The abilities they exhibit are called Siddhis in Hindu, while in Buddhism they are called Iddhi. There are also correlates in Jainism and Sikhism.
These Siddhis commonly use knowledge gained through Sādhanā, Tantras, meditation, and the manipulation of Prana (Qi, Ki, or Chi in Buddhist belief).
In the West, practitioners are called Yogis or Mystics (Mystic from French mystique, Old French mistique, Latin mysticus, and originating with Ancient Greek mustikos (secret, mystic) and mustes (one who has been initiated).
So I prefer Mystic, or Siddhas, for psionicist/psion, and call psi/psionics either Prana or Sādhanā.