Cousin vs. Vetter
Both Cousin and Vetter translate to the English word for a male cousin, meaning the son of an aunt or uncle. The primary difference is their usage and age. Cousin is the universally used modern standard term, while Vetter is an older, native Germanic word that is now mostly considered old-fashioned, literary, or regional.
Cousin
The word Cousin is the modern, standard term used for a male cousin in everyday German. Borrowed from French, it is understood universally across all German-speaking regions and is the primary word you should use in contemporary casual or formal conversations.
Mein Cousin studiert Medizin in Berlin.
(My cousin is studying medicine in Berlin.)
Wir haben unseren Cousin seit fünf Jahren nicht mehr gesehen.
(We have not seen our cousin in five years.)
Der kleine Hund gehört dem Cousin meiner besten Freundin.
(The small dog belongs to the cousin of my best friend.)
Ich spiele jeden Samstagnachmittag Tennis mit meinem Cousin.
(I play tennis with my cousin every Saturday afternoon.)
Sie hat beschlossen, zusammen mit ihrem Cousin ein neues Restaurant zu eröffnen.
(She decided to open a new restaurant together with her cousin.)
Vetter
The word Vetter is a traditional Germanic word for a male cousin that has largely become old-fashioned. Today, it is primarily found in classical literature, historical contexts, specific idioms, or occasionally in southern regional dialects.
Die beiden Monarchen waren Vettern ersten Grades.
(The two monarchs were first cousins.)
Mein Großvater erzählte oft Geschichten über seinen Vetter aus Amerika.
(My grandfather often told stories about his cousin from America.)
Nach alter Tradition erbte der älteste Vetter das Hofgut.
(According to old tradition, the oldest cousin inherited the estate.)
Ein entfernter Vetter der Familie meldete unerwartet Anspruch auf das Erbe an.
(A distant cousin of the family unexpectedly laid claim to the inheritance.)
In dem historischen Roman kämpft der junge Held gegen seinen eigenen Vetter.
(In the historical novel, the young hero fights against his own cousin.)
Summary
In short, Cousin is the modern, everyday word you should actively use when speaking German today. You only need to understand Vetter passively, as you will mostly encounter it in older books, historical documentaries, or specific regional phrases.