Sometimes a whole short word like 'the' or 'she' can be a morpheme; but morphemes are not necessarily whole words in themselves. -s' as a marker of plurals in nouns in English is a morpheme; so are the participle endings '-ing' and '-ed'. Prefixes like 'un-' and suffixes like '-ment' are also morphemes. They cannot be used as words in their own right, but all speakers of English know what they mean - and all competent native speakers can use them, both correctly in existing words and creatively, in new words.
Units like single letters or sounds are not in themselves morphemes. But in certain uses single letters do have a meaning, and are treated as morphemes. The single letter '-a-', for example, is a morpheme in words like 'amoral' (~ 'without morals'). It reflects a Greek negative, and has the meaning 'not'. As a self-contained letter (a single word), too, 'a' is a morpheme - if a different one. Here, it is the indefinite article.
Of course, this does not mean that the letter 'a' is a morpheme. It isn't. It can't be. Consider that the whole richness of the English language can be written down with only 26 letters, and you will realise that not one of them is always a morpheme. Like so much in the study of language, it depends on the context and the actual usage.
Morphemes can be divided into several classes. The two most useful for beginners in the study of language are:
- Lexical morphemes - the units of word-building. These are the bits out of which words are made. They are the equivalent of form, or lexical, words (see Word class in the Grammar course) - they are to do with meaning.
- Inflectional morphemes - the units that go to show the grammatical uses of words; they do not have much meaning as such (like function words).