The words 'jou' and 'joune' seem to have the same meaning, but different uses. Can you clarify this?

They practically carry the same meaning.

jou - the day
jounen - the (duration of the) day

Examples:
Have a great day. - Pase yon bon jounen.

I had a bad day. - M te pase yon move jounen.

On what day are you coming?  - Ki jou wap vini?

Today is the first day of the year. -Jodi a se premye jou mwa a.

Today is the last day of the year. - Jodi a se dènye jou ane a.

She cried all day. - Li te kriye tout la jounen.

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