There is really no significant difference between these usages. It's mostly a matter of personal preference. Take "early/later" vs "early/later on". If I was talking about the passage of time during the day, I'd probably use "early that day" and "later that day"; whereas if I was referring to someone's career, I'd say "early on in his career" and "later on in his career". However, switching them round would be just as correct. Don't worry about it.