On A Practical Guide to Lexicography (2003), edited by Piet van Sterkenburg, the first type of dictionary is referred as dictionary.
For us, looking for a definition of ‘dictionary’ is looking for a definition of the prototypical dictionary. The prototypical dictionary is the alphabetical monolingual general-purpose dictionary. Its characteristics are the use of one and the same language for both the object and the means of description, the supposed exhaustive nature of the list of described words and the more linguistic than encyclopaedic nature of the knowledge offered. The monolingual general-purpose dictionary . . .
contains primarily semasiological rather than onomasiological or non-semantic data, gives a description of a standard language rather than restricted or marked language varieties, and serves a pedagogical purpose rather than a critical or scholarly one.
What makes the monolingual general-purpose dictionary so prototypical? I will continue here on the course set out by Béjoint (2000:40):
It is the one that every household has, that everyone thinks of first when the word dictionary is mentioned, it is the type that is most often bought, most often consulted, the one that plays the most important role in the society that produces it. (Page 3)
The second type of the dictionary is referred as multilingual or translation dictionary.
According to Zgusta (1971:294) the basic aim of multilingual or translation dictionaries is ‘to co-ordinate with the lexical units of one language those units of another language which are equivalent in their lexical meaning’. On the microstructural level this function is realised by providing for a lemma in the source language one or more translation equivalents in the target language. (Page 67)