The same linguistic term (ie the universal in dicendo) can be attributed to various subjects in three diverse ways: univocally, equivocally, analogically. There are three types of universality of names, which St. Thomas explains thusly:
sciendum quod aliquid praedicatur de diversis multipliciter:
[A] quandoque quidem secundum rationem omnino eamdem, et tunc dicitur de eis univoce praedicari, sicut animal de equo et bove.
[B] Quandoque vero secundum rationes omnino diversas; et tunc dicitur de eis aequivoce praedicari, sicut canis de sidere et animali.
[C] Quandoque vero secundum rationes quae partim sunt diversae et partim non diversae: diversae quidem secundum quod diversas habitudines important, unae autem secundum quod ad unum aliquid et idem istae diversae habitudines referuntur; et illud dicitur 'analogice praedicari', idest proportionaliter, prout unumquodque secundum suam habitudinem ad illud unum refertur.
SM 4, lect. 1, n. 535
But it must be noted that a term is predicated of different things in various senses.
[A] Sometimes it is predicated of them according to a meaning which is entirely the same, and then it is said to be predicated of them univocally, as animal is predicated of a horse and of an ox.
[B] Sometimes it is predicated of them according to meanings which are entirely different, and then it is said to be predicated of them equivocally, as dog is predicated of a star and of an animal.
[C] And sometimes it is predicated of them according to meanings which are partly different and partly not (different inasmuch as they imply different relationships, and the same inasmuch as these different relationships are referred to one and the same thing), and then it is said “to be predicated analogously,” i.e., proportionally, according as each one by its own relationship is referred to that one same thing.
SM 4, lect. 1, n. 535
Let us explain per partes.
[A] A univocal term signifies one concept, whose meaning is always the same. Cf. De principiis naturae 6, n. 366:
Univoce praedicatur quod praedicatur secundum idem nomen et secundum rationem eamdem, idest definitionem, sicut animal praedicatur de homine et de asino. Utrumque enim dicitur animal, et utrumque est substantia animata sensibilis, quod est definitio animalis.
In the example cited by St. Thomas, the term 'animal' symbolizes only the concept of 'animal', which signifies always and only 'corporeal living sensitive substance'.
[B] An Equivocal term signifies two or more concepts, each of which has its own meaning, different from those of the others. Cf. loc. cit.:
Aequivoce praedicatur, quod praedicatur de aliquibus secundum idem nomen, et secundum diversam rationem: sicut canis dicitur de latrabili et de caelesti, quae conveniunt solum in nomine, et non in definitione sive significatione: id enim quod significatur per nomen, est definitio
St. Thomas gives as an example "dog", which can refer to the domestic animal or to the constellation. It should be noted that only the term can be equivocal, not the concept, because the latter always bears a certain unity of signification.
[C] An analogical term signifies one concept, whose meaning is partially one and partially many. For example, the term "life" signifies a concept, that of 'life', whose meaning is one insofar as it refers to a substantial reality endowed with a proper operation, but the meaning itself is many insofar as there are various modes essentially varied of being alive (as a plant, as an animal, as a man, as an angel, as God).
It can be seen that, as concerns the concept, only two (and not three) general modes of predicability are possible: univocity and analogy. We should now examine in detail these two types of conceptual universality.