At http://www.thefreedictionary.com/duck, both the AHDEL and Collins claim that there are four English words 'duck'. They distinguish them by right-superscripts (which device is restricted to such analyses, of course).
The one they both choose to label duck³ (a heavy cotton fabric) is obviously not related to the other three – this is a case of convergent evolution, from different sources. Different etymologies.
Although words 1, 2 and 4 are obviously etymologically related to each other (word 4 in a punning way), they are still considered to have diverged sufficiently to be classed as three further isoformal words (same spelling; these also have the same pronunciation) - homonyms (strict definition).
However, if we delve deeper, and look, for instance, at AHDEL's treatment of duck³, we see that it lists two (closely related) senses (admittedly one existing only in the plural form and the other almost invariably in the singular) – ONE the material and TWO clothing (usually trousers) made from that material. These senses are classed as not being separate words. Different senses of the same word are known as polysemes. An obvious example: to play football, you need a football.
Sadly, I have not come across a consensus on whether polysemy is a term that is allowed to be applied to isoformal / homographic orthographic words of different word-classes (eg house (n) and house (v); round (preposition) and round (adj) etc).
Oh, and in answer to the second question – an orthographic word is 'a meaningful (within the parameters of the language being used) string of letters bounded by spaces'.
The term lexeme covers 'families' of 'the same word' , so man = man & men; go = go, goes ...
Edwin Ashworth