Lexemes and word forms
The term "word" is ambiguous in common usage. To take up again the example of dog vs. dogs, there is one sense in which these two are the same "word" (they are both nouns that refer to the same kind of animal, differing only in number), and another sense in which they are different words (they can't generally be used in the same sentences without altering other words to fit; for example, the verbs is and are in The dog is happy and The dogs are happy).
The distinction between these two senses of "word" is arguably the most important one in morphology. The first sense of "word," the one in which dog and dogs are "the same word," is called lexeme. The second sense is called word-form. We thus say that dog and dogs are different forms of the same lexeme. Dog and dog-catcher, on the other hand, are different lexemes; for example, they refer to two different kinds of entities. The form of a word that is chosen conventionally to represent the canonical form of a word is called a lemma, or citation form.