Cognate (n.): a word which shares root and meaning with a word in another language.
The word comes from the same root as "recognize," and basically refers to words that you can recognize in another language without learning anything about that language. The term is often used informally to refer to words that mean the same thing and look or sound similar in two languages.
Examples:
padre, father
municipio, municipality
The first example is technically a Spanish/English cognate pair, but many people would not call it such. The second example shows what most people would call a cognate pair. The second pair is truly a cognate pair, but not because of its similarity in appearance. Similarity of appearance is only a positive side effect (and not a consistently present one) of cognates, technically speaking.
False cognate (n.): a word which appears to share root and meaning with a word in another language. The word does not share meaning, though it may share root.
This also is used informally, referring to words in different languages that look similar, but do not share meaning. Here appearance is a factor because the reader follows misleading cues regarding the translation of the word into his/her first language.
Examples:
fabric, fábrica
embarrassed, embarazada
Both pairs are false cognates, but the second pair is probably a former cognate. Former cognates (which share root and appearance but not meaning) are a subset of false cognates. These words at one time shared meaning as well, and therefore were true cognates, but since then one or both have changed in meaning and are now false cognates.
To clarify:
root + meaning + appearance = cognate/true cognate
root + meaning - appearance = cognate/true cognate
root - meaning + appearance = false cognate (former cognate)
root - meaning - appearance = etymologically-related word
meaning + appearance - root = technically not a cognate, but many would call it one
meaning - root - appearance = translation
appearance - meaning - root = false cognate
One other possibility is when a word is borrowed directly from one language into another. In this case, the technical definition of a cognate fits, but it would be better to call it a borrowing/Anglicism/Spanishism/etc. (which should generally be considered a subset of cognates). In the best case, this is an exact copy of the word in the other language (though changes of spelling to make it fit the receiving language are common and perfectly appropriate), including any secondary meanings. The best case is very rare. Generally, very few of the meanings are transferred--often only one, which is frequently not one of the principle meanings in the source language. But this is fairly natural and regular. The problem here arises when a borrowing is incomplete or incorrect.
A good example of this is the English --> Spanish borrowing "esmokin." This word is taken from the term "smoking jacket" in English. Two errors appear here: a) the term in Spanish has come to refer to a tuxedo or very formal suit, and not to the jacket used to protect one's clothes while one is smoking, and b) the wrong word was set upon when the borrowing was made: the word should have been "jacket" (which has its own borrowing [or cognate], "chaqueta") or even better, the entire term, but unfortunately only the adjective was chosen, which really has little to do with the article of clothing itself, much less a tuxedo (as it is now used).
A good example of borrowing of only one or two meanings of a word is the Spanish --> English borrowings "burro" and "burrito." In Spanish, "burro" refers to a small horse-like animal commonly used as a beast of burden. There is a food in Mexico by this name because someone thought that the food looked like the animal. "Burrito" refers to a smaller one of either of these. Unfortunately, English-speakers, having only limited contact with the language, took "burro" to refer only to the animal (perhaps when it was borrowed, the food did not yet exist), and later took the word "burrito" to refer only to the food, without noting any connection between the terms, regardless of the obvious connection in the source language. Thus, in English there are two separate, unrelated words for these things, while in Spanish, the terms are directly related and more or less interchangeable.
