You can use "gomennasai" to apology for your impoliteness or for yourself's false. You also can use as greeting words when you come or leave people's house. "Sumimasen" , or "sumanai" is used when you want to apology or request s.o (you think this will be bad for listener)

sumimasen means excuse me, use the same way as excuse me in english application: excuse me (sumimasen), are you Michael? gomennasai means sorry, but it is not exactly means sorry in english.