Text count
Text count, to follow Wiki’s scheme, is a number of  words, lines, characters (with or without spaces), pages or other defined units in a text.Word
Yes. Although it may seem ridiculous, we often can’t define what actually a word for the counting engine is. For example, for Word processor a word is everything between two spaces, including numbers. Smarter word count tools can make the difference between the words and other symbols, allowing a word to be a word in its offline meaning.

Word limit
Is often used by editors to define the length of the desired text.

Source word count

As translators are usually charged per source word, a source word count is needed to know the number of words in the source text. If a translator can’t count words in a source text (i.e. hard copies), the payment is set by the target word count.

Target word count -

the number of words in a translated document.

Hope it wasn’t too many terms for 1 post. But I’m still wondering about all the “footers, headers, notes, footnotes, end notes, text boxes, shapes, embedded and linked documents, comments and hidden text”. Are you?