A fundamental difference in theoretical models of morphology and, particularly, of the syntax–morphology interface is that between endoskeletal and exoskeletal approaches. In the former, more traditional, endoskeletal approaches, open-class lexical items like cat or sing are held to be inherently endowed with a series of formal features that determine the properties of the linguistic expressions in which they appear. In the latter, more recent, exoskeletal approaches, it is rather the morphosyntactic configurations, independently produced by the combination of abstract functional elements, that determine those properties. Lexical items, in this latter approach, are part of the structure but, crucially, do not determine it.
Conceptually, although a correlation is usually made between endoskeletalism and lexicalism/projectionism, on the one hand, and between exoskeletalism and (neo)constructionism, on the other, things are actually more complicated, and some frameworks exist that seem to challenge those correlations, in particular when the difference between word and morpheme is taken into account.
Empirically, the difference between these two approaches to morphology and the morphology-syntax interface comes to light when one examines how each one treats a diversity of word-related phenomena: morphosyntactic category and category shift in derivational processes, inflectional class, nominal properties like mass or count, and verbal properties like agentivity and (a)telicity.