오늘(o-neul, oneul)
A time expression referring to the current day
When to use
current date mention, events happening today, plans for today, deadline today
The nuance
오늘 refers to the date of the moment of speaking and can include past or future events within the same day, but always the current calendar day.
내일(nae-il, naeil)
A time expression referring to the day after today, the next calendar day
When to use
next day mention, plans for tomorrow, appointments tomorrow, deadline tomorrow
The nuance
내일 means the day after today and is used for any situation occurring on the next calendar day after today ends.