미안해요 is everyday polite for friends and coworkers. 죄송합니다 is more polite and respectful for strangers, customers, elders, or serious mistakes.
미안해 is casual. Use it only with close friends or younger people. To be safe and polite, use 미안해요.
Say 괜찮아요 (gwaenchanayo) - It's okay, or 아니에요 (anieyo) - No worries.
미안해요 means "I'm sorry" in a polite everyday way. 미안하다 (mianhada) = to be sorry, → 미안해요 = polite form. Most common apology to friends, family, coworkers. For deeper respect use 죄송합니다.
1. Small mistake to friend: 미안해요
2. Work / elder: 미안합니다 or 죄송합니다
3. Customer / stranger: 죄송합니다 (most respectful)
I'm sorry. I'm late.
I'm really sorry. I'll be careful next time.
I'm sorry. I won't do it again. (Very polite)
Sorry, it's my fault. (Casual)
• 괜찮아요 (gwaenchanayo) - It's okay (reply to sorry)
• 죄송해요 (joesonghaeyo) - Sorry (polite but less formal than 죄송합니다)
• 실수했어요 (silsuhaesseoyo) - I made a mistake