English for Today by Ganiu Abisoye Bamgbose (Dr GAB)

Your half brother or your step brother?

Although his mum had him before marrying my dad, no one would know we are ~half brothers~ (nonstandard).
Although his mum had him before marrying my dad, no one would know we are *step brothers* (standard).
A stepbrother is the son of your stepmother or your stepfather. You do not share any blood relation with a stepbrother.

I am so close with my ~step brother~ that you would not know we are only of the same dad (nonstandard).
I am so close with my *half brother* that you would not know we are only of the same dad (standard).
A half brother is a boy or man who shares only one biological parent with you. He is your half-brother if you have the same mother but different fathers, or the same father but different mothers.
GAB