What is the correct nomenclature for languages constructing logical functions through desinences (through declensions) and what for the ones doing it via prepositions?
A language with a certain degree of inflection is called synthetic language. The subsets are highly inflected and weakly inflected.
A synthetic language which has derivational morphology so that the complex words become synthesized by concatenation of unchanged morphemes is called agglutinative language.
If the bound morphemes serve several roles at once (e.g., person+case or gender+time) and therefore change, that would be a fusional language.
In the above cases, the prefixes are not considered separately because usually, all types of affixes serve the common role in the morphology.