Usually, the sentence, "I'm American", is used. Is it OK if I say,"I'm an American." instead of "I'm American"? If not, why? What's the difference?
"I'm American" means 'My nationality is "American" '.
"I'm an American" means '(There are many citizens in America and) I am one of them".
American, as adjective, refers to one of my attributes, that is
An American, as noun, refers to the entity "American citizen". I am such an entity.
I'm American means that you are American, the adjective form. This means relating to America.
I'm an American means that you are an American, the noun form. This means that you are a person from America.
On Dictionary.com, it says this:
of or relating to the United States of America or its inhabitants.
of or relating to North or South America; of the Western Hemisphere.
of or relating to the aboriginal Indians of North and South America, usually excluding the Eskimos, regarded as being of Asian ancestry and marked generally by reddish to brownish skin, black hair, dark eyes, and prominent cheekbones.
a citizen of the United States of America.
a native or inhabitant of the Western Hemisphere.
an Indian of North or South America.
a steam locomotive having a four-wheeled front truck, four driving wheels, and no rear truck.
The definition that are relevant to this question would probably be defintions 1 in the noun and adjective forms.
Saying I'm an American would be fine.