人家 vs 别人 (others — colloquial vs neutral)

Others — with attitude, or without

• Both can mean "other people" — but other people人家rén jiā has extra colours.
• other people别人bié rén = other people (neutral, "someone else").
• other people人家rén jiā = (colloquial) other people, a specific person — or even a coy "me".

other people别人bié rén = others (neutral)

• other people别人bié rén(of / 's)的dematter事shì，no matter (who, what etc)别管bié guǎn = "other people's business — don't meddle."

this这zhèis是shìother people别人bié rén的debusiness事shì。

• other people别人bié rén(of / 's)的dematter事shì = "someone else's business."

other people人家rén jiā = others / a person / coy "me"

• other people人家rén jiāall / both都dōuto walk走zǒu(completed / change)了le = "everyone else has left"; other people人家rén jiānot不bùto tell告诉gào sùyou你nǐ = "I'm not telling you (pouting)."

they人家rén jiaall都dōuleave走zǒu了le。

• other people人家rén jiāall / both都dōuto walk走zǒu(completed / change)了le = "everyone else has gone."

Recap

Read the full reference: HSK 6 grammar — Comparing similar nouns.