Two Approaches to Morphology: Item-and-Arrangement, Item-and-Process
Hockett (1954) distinguishes between two basic approaches to morphology, which he calls item-and-arrangement and item-and-process. Both are associated with American structuralist linguistics, codified by Bloomfield (1933), but continue to be important today. Item-and arrangement and item-and-process represent two distinct points of view. Item-and-arrangement proceeds from a picture of each language as a set of elements and the patterns in which those elements occur. The item-and-process picture gives no independent status to the items, which arise instead through the construction of the patterns.
Item-and-arrangement grew out of the structuralists’ preoccupation with word analysis, and in particular, with techniques for breaking words down into their component morphemes, which are the items. Morphology is then seen as the arrangement of these morphemes into a particular order or structure. For example, books results from the concatenation of the two morphemes book and -s.
Item-and-process, as its name suggests, is an approach to morphology in which complex words result from the operation of processes on simpler words. Working in an item-and-process model, we might say that books results when the lexeme book undergoes the function ‘make plural’. In regular cases, this function will add the segment /-z/ (cf. photos, lions), which is realized as /-s/ after most voiceless segments (cf. giraffes), and as /-əz/ after sibilants and affricates (cf. roses).
Item-and-arrangement and item-and-process are almost equivalent to one another mathematically. Everything you can express in item-and-arrangement can be expressed in item-and-process, and almost anything you can express in item-and-process can be expressed in item-and-arrangement. It just depends on what you regard as an item. For example, if you allow items to have a negative value (on the analogy of negative numbers like −1), then even subtractive morphology of the sort seen in the formation of the Papago (Uto-Aztecan) perfective (13) can count as item-and-arrangement (data from Zepeda 1983: 59ff., cited in Anderson 1992: 65):1

In (13) we see that the Papago perfective is generally formed by removal of the final consonant of the imperfective, regardless of what consonant it is. It might seem counterintuitive to think of this deleted consonant as a segment with some particular value, parallel to the English past tense marker -ed, but mathematically, such a negative entity is not difficult to imagine. We could think of the affix as something like a negative final consonant.
Despite the mathematical similarity of the item-and-process and item-and-arrangement approaches, many morphological phenomena do not fit neatly into the latter. Papago perfective formation is one example. We can imagine a negative affix, but its plausibility is questionable.
1 The perfective and imperfective are two forms of the verb. As a first approximation, we may say that the perfective expresses an action as being complete, while the imperfective expresses an action as being incomplete.