The wedding is the official ceremony/party. (The party is usually called the "reception"):
I'm going to my cousin's wedding on October 7.
We want to have a band at our wedding reception.
The wedding will be at the church, and the reception will be at a restaurant. The marriage is the relationship in general, or the institution in society:
My parents have a strong marriage. They've been together for 35 years.
New York has just legalized gay marriage.
Over 40% of marriages end in divorce.
The word married describes the status of a person. Use married to (not "married with") when you describe the person's husband/wife:
My sister isn't married. She's single.
I've been married for 5 years.
He's married to a woman from another country.
She's married to a successful businessman.
We use marry or get married for the action of formalizing the marriage:
He married a woman he'd known since high school. They finally got married after dating for ten years.
She's going to marry a famous actor. They're getting married next month.
Science Facts
In 1822, Dr. William Beaumont studied human digestion as it happened, through a hole in the side and stomach of a patient who had been shot. The hole did not heal, allowing Dr. Beaumont to study, but also allowing food and drink to ooze out if it was not covered up. .. More >>