When you enter a formal event with the dress code business formal, make sure that you are in full suit. The suit should be more conservative and colors such as navy or black are appropriate. Both men and women should wear a clean, pressed, (formal) button down shirt with a collar. The shirt must be worn tucked in. Stockings are a must for women, a tie and belt are required for men, and a jacket and closed-toed shoes are required for both.
When the dress code is business casual, you do not have to wear a full suit. Women should wear slacks or a skirt, a blouse or shirt with a collar and closed-toe shoes. For men, business casual usually means slacks or khakis, with a (formal) button down shirt with a jacket but no tie. The shirt should be tucked in.