In counting vocabulary one counts headwords, lemmas or word families. These terms mean more or less the same thing. It just recognises that essentially the same word may appear in different forms.
A person's vocabulary is all the words that he or she knows. A five year old would probably know about 4,000 to 5,000 words. An adult who has studied at university or college may know at least 20,000 words in their language.
The number of actual words in a language is vastly larger than this. Both the Oxford English Dictionary and Webster's Third New International Dictionary have about half a million headwords. But each has many words which the other does not. On that basis, it is believed that the two together cover about 750,000 words. And there may be more than that.
How do we manage with so few words? Because everyday speech uses quite a small vocabulary. Knowledge of the 3000 most frequent English word families gives an understanding of 95% of word use. It is a fact that the most common words are also the shorter words, and this is true in all languages. A list of the 50 most common words in English has no words longer than six letters, and more than half have no more than three letters.
The vocabulary of a language is always changing. New words are invented or words change their meaning. This means that dictionaries have to be updated. Words to do with computers such as "download" are new to the English language. The new word "bling" came from hip hop. Words like "cool" have developed new meanings.
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- Headwords are the words in bold in a dictionary.
- A word family includes a base word, its inflected forms, and a small number of reasonably regular derived forms. Bauer L.& Nation I.S.P. 1993. Word families. International Journal of Lexicography 6, 4: 253-279.
- Nation, Paul, and Robert Waring. "Vocabulary size, text coverage and word lists." Vocabulary: Description, acquisition and pedagogy (1997): 6-19. 
- Goulden R; Nation P. & Read J. 1990. How large can a receptive vocabulary be? Applied Linguistics 11: 341-363.
- Crystal, David 1995. The Cambridge encyclopedia of the English language. Cambridge University Press, p119, p423.
- Adolphs and Schmitt 2003. Lexical coverage of spoken discourse. http://applij.oxfordjournals.org/content/24/4/425.full.pdf+html
- Zipf G.K. 1949. Human behavior and the principle of least effort. Cambridge, Massachusetts: Addison-Wesley.
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