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Frère vs. frangin

The French words frère and frangin both mean brother. The main difference between them lies in their level of formality and the context in which they are used.

Frère

A1
This is the standard, neutral, and most common word for brother. It is appropriate for all situations, from formal to informal, and can be used when talking to or about your brother in any context.
J'ai un frère plus âgé et une sœur plus jeune.
(I have an older brother and a younger sister.)
Mon frère arrive demain pour le week-end.
(My brother is arriving tomorrow for the weekend.)
Le fils de mon oncle est aussi mon cousin, pas mon frère.
(My uncle's son is also my cousin, not my brother.)
Lors de la cérémonie, il a remercié son frère pour son soutien.
(During the ceremony, he thanked his brother for his support.)
Dans de nombreux ordres religieux, les hommes s'appellent frère.
(In many religious orders, the men call each other brother.)

Frangin

B1
This is a very informal, colloquial, and often affectionate term for brother. It is similar to saying bro in English. You would only use frangin in casual conversations with family, close friends, or your brother himself.
Je vais voir un match de foot avec mon frangin ce soir.
(I'm going to watch a soccer game with my bro tonight.)
, frangin, tu peux m'aider à porter ça ?
(Hey, bro, can you help me carry this?)
Mon frangin m'a offert un super cadeau pour mon anniversaire.
(My bro gave me a great gift for my birthday.)
Alors, qu'est-ce que tu deviens, frangin ?
(So, what have you been up to, bro?)
On ne s'est pas vus depuis des lustres, mon vieux frangin !
(We haven't seen each other in ages, my old bro!)

Summary

In essence, frère is the universal and standard word for brother suitable for any context. Frangin is its informal, colloquial, and affectionate counterpart, equivalent to bro, and should be reserved for casual, familiar situations.