Party Definitions

A Black Tie invitation calls for formal attire. Men wear tuxedos, women wear cocktail, long dresses or dressy evening separates.

Formal usually means the same as Black Tie, but in some trendier cities like New York or Los Angeles, it could mean a black shirt, no tie with a tux. Women wear cocktail, long dresses or dressy evening separates.
More about formal dresses: Formal Dresses Under $100 A White Tie or Ultra-formal invitation requires men wear full dress, with white tie, vest, shirt. Women wear long gowns.
More about dressing up: Get Party Perfect in 5 Days

Black Tie Optional

A Black Tie Optional or Black Tie Invited gives you the option of wearing a tuxedo or formal dress, but it should clue you into the formality of the event, meaning a dark suit and tie would be your other option. Women wear cocktail, long dresses or dressy evening separates.

Creative Black Tie

Creative Black Tie leaves room for trendy interpretations of formal wear. He can go more modern with a tux -- maybe a black shirt, no tie. She wears long or short dresses or evening separates.

Sometimes, themed parties call for dress codes like Texas Black Tie or other variations of Creative Black Tie. In that situation, you can have more fun with it, choosing a dressy look with a theme (for him, it could be a tux with boots and for her it could be a long dress paired with Southwestern style silver belt and jewelry).

Semi-Formal

Semi-Formal or After Five means that tuxes are not required, nor are long dresses. An evening wedding (after 6 PM) would still dictate dark suits for him, and a cocktail dress for her. Daytime semi-formal events mean a suit for him and an appropriate short dress or dressy suit for her.

Business Formal is the same as Semi-Formal for him, but for women it suggests that women opt for more tailored dressy suits and dresses (nothing too slinky or sexy).

Cocktail Attire

Cocktail Attire means short, elegant dresses for her and dark suits for him.
More about cocktail dresses: Best Little Black Dresses
10 Perfect Cocktail Dresses