brother-in-law:?小舅子/小叔子

connected by marriage.

e.g. You got married to someone and he/she had a brother. That’s your brother-in-law.

?

half-brother: 同父異母兄弟；同母異父兄弟

Your dad got remarried and had a son. That’s your half-brother.

?

step brother: 繼兄弟

the son of the person that your parent married.

?

adopted brother: 收養(yǎng)的兄弟

When your parents legally adopt somebody else. They become your brother.