Eugene Nida distinguishes two types of equivalence:

1. dynamic equivalence,
2. formal equivalence.

The dynamic equivalence attempts to convey the thought expressed in a source text (at the expense of literalness, original word order, the source text’s grammatical voice, etc., if necessary), while the formal equivalence attempts to render the text word-for-word (at the expense of natural expression in the target language, if necessary). The two approaches represent emphases, respectively, on readability and on literal fidelity to the source text. There is, however, in reality no sharp boundary between dynamic and formal equivalence.

Reference: E. Nida and C. Taber, The Theory and Practice of Translation, E.J. Brill, Leiden, 1969

Also Popovič operates a bipartition in defining untranslatability, but he does not make a distinction between the linguistic and the cultural. He distinguishes:

1. a situation in which the linguistic elements of the original cannot be replaced adequately in structural, linear, functional or semantic terms in consequence of a lack of denotation or connotation, and
2. a situation where the relation between the creative subject and its linguistic expression in the original does not find an adequate linguistic expression in the translation.

Reference: A. Popovič, A Dictionary for the Analysis of Literary Translation, University of Alberta, Edmonton, Alberta, 1976

In finding equivalence Anton Popovič distinguishes four types of translation equivalence:

1. linguistic equivalence, where there is homogeneity on the linguistic level of both SL and TL texts;
2. paradigmatic equivalence, where there is equivalence of the elements of a paradigmatic expressive axis;
3. stylistic (translational) equivalence, where there is functional equivalence of elements in both original and translation aiming at an expressive identity with an invariant of identical meaning;
4. textual (syntagmatic) equivalence, where there is equivalence of the syntagmatic structuring of a text.

Reference: A. Popovič, A Dictionary for the Analysis of Literary Translation, University of Alberta, Edmonton, Alberta, 1976

Untranslatability is a property of a text, or of any utterance, in one language, for which no equivalent text or utterance can be found in another language.
Catford divides untranslatability in two types:

1. linguistic untranslatability, that occurs when there is no lexical or syntactical substitute in the TL for an SL item;
2. cultural untranslatability due to the absence in the TL culture of a relevant situational feature for the SL text.

Reference: J.C. Catford, A linguistic Theory of Translation: An Essay in Applied Linguistics, Oxford University Press, London, 1965

In his article On Linguistic Aspects of Translation (1959), Roman Jakobson distinguishes three types of translation:

1. The intralingual translation or rewording is the interpretation of verbal signs by means of other signs belonging to the same language.
2. The interligual translation or translation proper is the interpretation of verbal signs by means of verbal signs from another language.
3. The intersemiotic translation or transmutation is the interpretation of verbal signs by means of signs belonging to non-verbal sign systems.

Reference: R. Jakobson, “On Linguistic Aspects of Translation” in R.A. Brower (ed.), On Translation, Harvard University Press, Cambridge, Mass., 1959, pp. 232-9.