In email communications, I have seen use of 申し訳ございません when saying sorry. How this phrase has been constructed and how it is different from すみません。
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1For すみません: japanese.stackexchange.com/q/56772/7810 – broken laptop Sep 18 '19 at 7:12
It literally means "There is no excuse", or "I have no excuse". Let's break it down:
- 申{もう}す is the humbling version of 言{い}う
- 言{い}い訳{わけ} means "excuse, explanation"
- so 申{もう}し訳{わけ} is kind of a humbling version of 言{い}い訳{わけ}
- ございます (or 御{ご}座{ざ}います in kanis but that's very rare; ござる in plain form) is polite version of ある, so ございません is a more polite way to mean "there is not"
As a result, 申{もう}し訳{わけ}ございません literally means "I have no excuse", and therefore is a very polite way to say "I'm sorry".
On the other hand, すみません is written 済{す}みません in kanjis. 済{す}む can mean "to feel at ease", so 済{す}みません might be translated as "I feel bad [for what I did]", which basically means "I'm sorry".
To sum it up:
申{もう}し訳{わけ}ございません
I have no excuses
すみません
I feel sorry
Now as you may know, 申{もう}し訳{わけ}ございません is much more often used in formal contexts than すみません, which is not rude per se but would be considered not respectful enough in a working context, especially in emails.