Here is a paragraph that uses all of them: At that time, I was a young man. That's when I went I went to University. That time was a great time. At the time, I didn't have a care in the world. Back then, I felt like I could do anything. Back in the day, we all acted like kings and queens. In the past, I was able to speak more Korean than I can now. Ultimately they are very similar expressions, but some of them have nuance differences. Particularly "Back in the day" has more of a nostalgic feel. "In the past" can refer to someone's past OR refer to the distant past (e.g. In the past, Sejong the Great invented Hangeul). "At that time" references something you've already discussed. (I went to University a while ago. At that time, grunge music was cool.) Hope that helps!

That's when I was playing the game that's when my dad came in my room and started yelling That time remember that time when we went the basketball game? At the time I couldn't call you at the time you asked because I was at work Back then I was a different person back then, I've changed Back in the day remember back in the day when you fell and broke your wrist? In the past Yeah I remember, but that's in the past. I'd rather not remember!! some of these are different ways to say the same thing.

yes!

Do you want examples on how they're used?