Conversion is a key type of word-formation process in English, but the precise nature of the relation between base and derivative in conversion is rarely discussed, even if conversion is considered as a dynamic process. When it is considered explicitly, the relation has been described in terms of paradigmatic relations between lexemes, specifically homonymy or polysemy. This is usually without any specification of how converted words accommodate the conditions set by the definition of each of these relations, and as a special type of one or the other, because conversion-related words violate some of those conditions. This article is intended as a systematic review of the literature that discusses the relation between conversion-related words in English. We show that a wide range of proposals have been made to describe the relation: homonymy, heterosemy, homomorphy, zero-derivation (as a relation), polysemy, lexical extension, synsemy, hyponymy and paronymy. We review the extent to which each of these terms fits the relationship in major types of conversion, and argue that, if a relationship is to be described between conversion-related pairs, then Cruse's (1986) separation of semantic relations of a paradigmatic type from paronymic relations is of special relevance here. We propose that, regardless of the direction and type of meaning, paronymy applies across the various specific semantic patterns that conversion may involve. We emphasize, however, the possibility of several relations according to the type of conversion, i.e. different types of conversion may need description in terms of a different relation.