The omniscient mind (rnam-mkhyen) of a Buddha has no conceptual cognition (rtog-pa), thus it does not mentally label anything with categories, but it does have designation (ming btags-pa). For limited beings (sems-can, sentient beings), designation is always conceptual; it involves not just a word or name (ming), but also a meaning category (don-spyi). For a Buddha, mental labeling is non-conceptual. It has only words or names, and they would be in all languages, but without any meaning categories.
When a Buddha sees a conventionally existent tree, his untainted aggregate of distinguishing (zag-med ‘du-shes-kyi phung-po) distinguishes the defining characteristic (mtshan-nyid) and knows that it is designated by the word for tree in all languages and that its conventional existence is accounted for merely in terms of what these names refer to. But a Buddha does not veil with a meaning category this cognition of the word and the object on which it is designated.
A Buddha has five purified aggregates, and so a purified aggregate of the six types of consciousness. According to the Jetsunpa (rJe-btsun Chos-kyi grags-pa) textbook tradition, all these six types of consciousness of a Buddha are omniscient. According to the Panchen (Pan-chen Blo-bzang grags-pa) textbook tradition, only a Buddha’s mental consciousness is omniscient; the five sensory consciousnesses are not omniscient. If it is an omniscient mind, it is constructive, but the five types of sensory consciousness are unspecified and so they cannot be an omniscient mind.