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.
Fact
The first airline, DELAG, was established on October 16, 1909, to carry passengers between German cities by Zeppelin airships. Up to November 1913, more than 34,000 people had used the service. .. More >>