expression
I'm sorry; I apologize
A formal, polite apology used in business and serious situations. Stronger than すみません.
ご迷惑をおかけして、申し訳ありません。
I am sorry for causing you trouble.
返信が遅くなり、申し訳ありません。
I apologize for the late reply.
expression
Used to express deep gratitude, often when someone has gone out of their way to help. Conveys a sense of indebtedness.
わざわざお越しいただき、申し訳ありません。
Thank you very much for coming all this way.
Less formal than 申し訳ありません; used for lighter apologies, getting attention, or expressing casual thanks.
More personal and less formal; used among friends, family, or for minor mistakes.
From 申し訳 (もうしわけ, 'excuse') + ありません (polite negative of ある, 'to exist'), literally 'there is no excuse'.