These two words can be used synonymously in some cases, but we can make some very simple distinctions if we treat kun as meaning only and bare and meaning just. 

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Kun | Only

Bare | Just

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Skal vi ikke tage ind til byen? | Shall we go out (to the city)?

Jeg vil gerne, men jeg har kun ti kroner på kontoen | I’d like to, but I only have ten kroners in my bank.

Jamen, så er det bare ærgerligt for dig | Well, then it’s just too bad for you.

Hej, hej! Bye bye! 

 

Lad os lave en kop te | Let’s make a cup of tea.

Skal vi ikke bare drikke vin i stedet? | Shouldn’t we just drink wine instead?

Hmm… Ja, okay. Det er trods alt fredag! | It is Friday, after all! 

Vi har faktisk kun vodka | But we actually only have vodka. 

Så er der fest! | Party time!