Morphological Typology
In the 19th century, philologists devised a now classic classification of languages according to their morphology. According to this typology, some languages are isolating, and have little to no morphology; others are agglutinative, and their words tend to have lots of easily separable morphemes; while others yet are inflectional or fusional, because their inflectional morphemes are "fused" together. This leads to one bound morpheme conveying multiple pieces of information. The classic example of an isolating language is Chinese; the classic example of an agglutinative language is Turkish; both Latin and Greek are classic examples of fusional languages.
Considering the variability of the world's languages, it becomes clear that this classification is not at all clear cut, and many languages do not neatly fit any one of these types, and some fit in more than one way. A continuum of complex morphology of language may be adapted when considering languages.
The three models of morphology stem from attempts to analyze languages that more or less match different categories in this typology. The Item-and-Arrangement approach fits very naturally with agglutinative languages; while the Item-and-Process and Word-and-Paradigm approaches usually address fusional languages.
The reader should also note that the classical typology mostly applies to inflectional morphology. There is very little fusion going on with word formation. Languages may be classified as synthetic or analytic in their word formation, depending on the preferred way of expressing notions that are not inflectional: either by using word formation (synthetic), or by using syntactic phrases (analytic).
Read more about this topic: Morphology (linguistics)