Gawd is a way of writing God when someone says it as a cry of surprise, fear, or strong feeling — “Oh my gawd!” — and the writer wants you to hear the sound, not a careful, church-like “God.” The vowel is drawn out and a bit theatrical. You meet it in comics, dialogue in stories, and jokey messages. It is the same word as God, only spelled to show how it was said: informal, sometimes comic, sometimes a little shocked. People also use this spelling when they want the feeling of the cry without writing the holy name in the usual way. It is not a separate idea, and it does not belong in careful school writing except when you are copying speech.