In linguistics, cognates are words that have a common etymological origin. In etymology, the cognate category excludes and loanwords. The word cognate derives from the Latin noun cognatus, which means "blood relative".
Cognates do not need to have the same meaning, which may have changed as the languages developed separately. For example English starve and Dutch sterven or German sterben ("to die") all derive from the same Proto-Germanic root, *sterbaną ("die"). English dish and German Tisch ("table"), with their flat surfaces, both come from Latin discus, but their later meanings are different. Discus is from Greek δίσκος (from the verb δικεῖν "to throw"). A later and separate English reflex of discus, probably through medieval Latin desca, is desk (see OED s.v. desk).
Examples of cognates in Indo-European languages are the words night (English), nuit (French), noche (Spanish), Nacht (German), nacht (Dutch), nag (Afrikaans), nicht (Scots), natt (Swedish, Norwegian), nat (Danish), nátt (Faroese), nótt (Icelandic), noc (Czech, Slovak, Polish), ночь, noch (Russian), ноќ, noć (Macedonian), нощ, nosht (Bulgarian), ніч, nich (Ukrainian), ноч, noch/noč (Belarusian), noč (Slovene), noć (Bosnian, Serbian, Croatian), νύξ, nyx (Ancient Greek, νύχτα/nychta in Modern Greek), nox/nocte (Latin), nakt- (Sanskrit), natë (Albanian), nos (Welsh), nueche (Asturian), noite (Portuguese and Galician), notte (Italian), nit (Catalan), nuèch/nuèit (Occitan), noapte (Romanian), nakts (Latvian), naktis (Lithuanian) and Naach (Colognian), all meaning "night" and being derived from the Proto-Indo-European *nókʷts "night".
Another Indo-European example is star (English), str- (Sanskrit), tara (Hindustani and Bengali), tora (Assamese), astre/étoile (French), ἀστήρ (astēr) (Greek or ἀστέρι/ἄστρο, asteri/astro in Modern Greek), astro/stella (Italian), aster (Latin) stea (Romanian and Venetian), stairno (Gothic), astl (Armenian), Stern (German), ster (Dutch and Afrikaans), Schtähn (Colognian), starn (Scots), stjerne (Norwegian and Danish), stjarna (Icelandic), stjärna (Swedish), stjørna (Faroese), setāre (Persian), stoorei (Pashto), seren (Welsh), steren (Cornish), estel (Catalan), estela (Occitan) estrella and astro Spanish, estrella Asturian and Leonese, estrela and astro (Portuguese and Galician) and estêre or stêrk (Kurdish), from the Proto-Indo-European *h₂stḗr "star".
Cognates may often be less easily recognised than the above examples, and authorities sometimes differ in their interpretations of the evidence. The English word milk is clearly a cognate of German Milch, Dutch melk, Russian молоко (moloko) and (Bosnian, Serbian, Slovenian mleko Croatian) also Montenegrin mlijeko. On the other hand, French lait, Catalan llet, Italian latte, Romanian lapte, Spanish leche and leite (Portuguese and Galician) (all meaning "milk") are less-obvious cognates of Ancient Greek γάλακτος gálaktos (genitive singular of γάλα gála, "milk"), a relationship that is more evidently seen through the intermediate Latin lac "milk" as well as the English word lactic and other terms borrowed from Latin. All of them come from Proto-Indo-European h₂melǵ- "milk".
Some cognates are semantic opposites. For instance, while the Hebrew word חוצפה chutzpah means "impudence," its Classical Arabic cognate حصافة ḥaṣāfah means "sound judgment." English black and Polish biały, meaning white, are cognates with opposite meanings, both deriving from the Proto-Indo-European *bʰleg- "to burn or shine".
Within the same language
Cognates within a single language, or doublets, may have meanings that are slightly or even totally different. For example, English ward and guard (<PIE *wer-, "to perceive, watch out for") are cognates, as are shirt (garment on top) and skirt (garment on bottom) (<PIE *sker-, "to cut"). In some cases, including this one, one cognate ("skirt") has an ultimate source in another language related to English, but the other one ("shirt") is native. That happened with many loanwords, such as skirt in this example, which was borrowed from Old Norse during the Danelaw.
Sometimes both doublets come from other languages, often the same one but at different times. For example, the word chief (meaning the leader of any group) comes from the Middle French chef ("head"), and its modern pronunciation preserves the Middle French consonant sound; the word chef (the leader of the cooks) was borrowed from the same source centuries later, but by then, the consonant had changed to a "sh" sound in French. Such word sets can also be called etymological twins, and of course, they may come in groups of higher numbers, as with, for example, the words wain (native), waggon/wagon (Dutch), and vehicle (Latin) in English.
A word may also enter another language, develop a new form or meaning there, and be re-borrowed into the original language; that is called reborrowing. For example, the Greek word κίνημα (kinima, "movement") became French cinéma (compare American English movie) and then later returned to Greece as σινεμά (sinema, "the art of film", "movie theater"). In Greece, κίνημα (kinima, "movement") and σινεμά (sinema, "filmmaking, cinema") are now doublets.
False cognates are words that people commonly believe are related (have a common origin), but that linguistic examination reveals are unrelated. For example, on the basis of superficial similarities, the Latin verb habēre and German haben, both meaning 'to have', appear to be cognates. However, because of the way words in the two languages evolved from Proto-Indo-European (PIE) roots, they cannot be cognate (see for example Grimm's law). German haben, like English have, comes from PIE *kh₂pyé- 'to grasp', and its real cognate in Latin is capere, 'to seize, grasp, capture'. Latin habēre, on the other hand, is from PIE *gʰabʰ, 'to give, to receive', and hence cognate with English give and German geben.
Likewise, English much and Spanish mucho look similar and have a similar meaning but are not cognates, as they evolved from different roots: much from Proto-Germanic *mikilaz < PIE *meǵ- and mucho from Latin multum < PIE *mel-.