In many scenes the term "Swing dancing" is used to refer generically to one or all of the following swing era dances: Lindy Hop, Charleston, Shag, Balboa and Blues.  For more details check here

http://en.wikipedia.org/wiki/Swing_Dance

What is East Coast Swing?

East Coast Swing has a 6 count basic step. This is in contrast to the meter of most swing music, which has a 4 count basic rhythm. In practice, however, the 6-count moves of the east coast swing are often combined with 8-count moves from the Lindy hop, Charleston, and Balboa.

What is Lindy Hop?

Lindy Hop also known as the Jitterbug has an 8 count basic step.

What's the difference between East Coast Swing, West Coast Swing, and Lindy Hop Swing?

• East Coast Swing, also known as triple step swing, triple timing swing, and jitterbug, has a basic count of 1, 2, 3&4, 5 & 6. Some folks describe the basic as "rock, step, triple step, triple step." Remeber that some instructors teach the step in reverse of the above.  This is a styling issue and neither way is right or wrong.  Use what works best for you.  ECS was the standard swing dance of 50's-era "sock hops." The music speed is 140-175 beats per minute. This dance has lilt (bounce) and energy. It is generally danced without strict regard to any particular orientation or geometry. It's easy to learn. When your parents talked about dancing the swing, this is probably the dance they were talking about.
   
• West Coast Swing is danced in a slot (a linear pattern) to slower music (generally 110-130 beats per minute). It's a smooth, often sexy dance, and it does not have lilt and bounce. West coast swing can be more difficult to learn because several foot patterns are required and the patterns may contain 6,8,and 10 or more counts. Common figures include 1) the push, 2) the left side pass, 3) the right side pass underarm turn, 4) tuck turn, 5) locked or "basket" whip, 6) regular whip, 7) back whip, and 8) reverse whip. West coast swing requires a very good sense of timing and connection.
   
• Lindy Hop Swing is the current rage with young people. Lindy hop swing can involve lots of kicks and aerials (lifts and flips). The dance uses six and eight count patterns. Common figures include the "swing out," and the Charleston step. Lindy hop dancers usually wear the black and white shoes and the guys might wear "Zoot Suits."

Do shoes Matter?

Yes, a pair of comfortable dance shoes makes all the difference.  Preferred shoes will have a leather or suede sole.  These shoes can be purchased online or at various dance shoe stores.  Additionally, you can have most shoes modified with suede soles at local shoe repair shops.

Where should I start?

Most people find East Coast Swing an easier start as it has a 6 count basic step. Lindy Hop is the next natural progression with an 8 count basic step.  Of course you can start anywhere if you want.  Start by taking weekly beginner classes until you feel comfortable with the steps.  Feel free to try new things and take risks with your dancing .  The more improvisation you can do the better off you will be but always remember your basic steps.