The designation itself has a history that the phrase's fame obscures.
The scheme of exactly four great sayings, one drawn from each of the four Vedas, is not in the Upanishads. It is a later doxographic arrangement, systematised within Advaita and used pedagogically, in which this statement from the Chandogya is paired with three others, aham brahmasmi from the Brihadaranyaka, prajnanam brahma from the Aitareya, and ayam atma brahma from the Mandukya. The neatness of one per Veda is the giveaway: it is a teaching device.
Later Advaita developed a further scheme distinguishing the four by grammatical person and function, treating one as instruction from a teacher, one as the pupil's realisation, and so on. This is genuine tradition and it is not Upanishadic.
What the Upanishad itself is doing in that chapter is closer to natural philosophy than to mysticism. The demonstrations are about what things are made of and whether a subtle cause can persist unperceived in its effect, the salt is invisible in the water and is present throughout it. The famous line arrives as the conclusion of a physical argument.
Modern usage tends to lift the three words entirely clear of the chapter and present them as a standalone assertion of the unity of the self and the absolute. That is a defensible tradition with over a thousand years behind it. It is not what a reader encounters on opening the text, and the difference is worth knowing about before deciding which one is being quoted.