Inflection vs. word-formation
Given the notion of a lexeme, it is possible to distinguish two kinds of morphological rules. Some morphological rules relate different forms of the same lexeme; while other rules relate two different lexemes. Rules of the first kind are called inflectional rules, while those of the second kind are called word-formation. The English plural, as illustrated by dog and dogs, is an inflectional rule; compounds like dog-catcher or dishwasher provide an example of a word-formation rule. Informally, word-formation rules form "new words" (that is, new lexemes), while inflection rules yield variant forms of the "same" word (lexeme).
There is a further distinction between two kinds of word-formation: derivation and compounding. Compounding is a process of word-formation that involves combining complete word-forms into a single compound form; dog-catcher is therefore a compound, because both dog and catcher are complete word-forms in their own right before the compounding process was applied, and are subsequently treated as one form. Derivation involves affixing bound (non-independent) forms to existing lexemes, whereby the addition of the affix derives a new lexeme. One example of derivation is clear in this case: the word independent is derived from the word dependent by prefixing it with the derivational prefix in-, while dependent itself is derived from the verb depend.
The distinction between inflection and word-formation is not at all clear-cut. There are many examples where linguists fail to agree whether a given rule is inflection or word-formation.