gomenasai and sumimasen

Does gomenasai and sumimasen mean the same thing? When should I use one or the other?

Gomennasai (I am sorry) is used only when you apologize privately.

Sumimasen (Excuse me) is more widely used, not only for light or formal apology but also in calling a person etc.

At least in my days, traditional girls' schools in Tokyo used to teach you that "sumimasen" is not a good expression. They told you that respectful people should use "gomennasai" or "moushiwake gozaimasen" or "shitsurei itashimashita". Even when speaking to a senior public, they told you you should use "gomennasai" rather than "sumimasen".

But nowadays, I notice that even older graduates are beginning to accept the term "sumimasen". Generally speaking, "gomennasai" tends to be more casual while "sumimasen" tends to be more distant.