Very Briefly and Compactly
West Coast patterns are inear "slot" and we explain by using a railroad track visual, while East Coast patterns are circular. This is a simple explanation just to get across the most visible differences. Trying to assign two basic style families to swing patterns and fit them all into east and west coast really isn't totally correct but it helps when trying to get a basic idea.
The most obvious differences between West Coast Swing and East Coast Swing are in the shape of their patterns.
East Coast Swing is circular with the couple moving around and around using some considerable space. The lead and follow movements generally mirror one another - where the lead takes a step left the follow takes a step right and so forth. East Coast Swing is often used in Jive choreography.
West Coast Swing moves up and down in a narrow "slot" taking a compact amount of room. Both patterns remain over the same area of floor space. The lead and follow generally do different things with the follow moving up and down the slot on in the railroad track and spinning and turning within it. The lead generally moves a smaller distance up and down the slot and moves around on the rails of the railroad track as the follower moves through the slot or on the tracks of the railroad.
These swing patterns also have a lot of variations under a number of names.
East Coast-type names include East Coast Swing, Jitterbug, Lindy hop, jive, and boogie-woogie.
West Coast-type names include West Coast Swing, Push, Whip, and Shag.
What we now call East Coast Swing dance is from the earliest patterns from the 20's and 30's. The Lindy Hop dance (Savoy style), Jitterbug dance and other swing dances of the period used a lot of room on the dance floor and were danced in the large ballrooms of the time. Now East Coast Swing cans be danced almost anywhere. After World War II swing music, swing dancing and dancing in general took an incredibly fast nosedive in popularity along with a loss of large ballrooms.
Dancing moved more into small club space and rhythm and blues music was more prevalent. These changes prompted development of West Coast swing which allowed for more dancers in a smaller area (with fewer people getting kicked by the dancers next to them). The linear pattern also worked better for bluesier, jazzier music. The somewhat slower music allowed dancers to express nuances of movement and feeling which were too hard to incorporate into the faster patterns.
The easiest pattern to pick up quickly is the East Coast Swing. A couple lessons and you will be on your way. The West Coast is a little trickier to get on to but with a few lessons and some minor effort you can be doing a West Coast in blues places and "expressing" your jazzier feelings in no time. Of the two patterns West Coast is arguably more adaptable to a wider variety of music although both can handle a wide array of music types and speeds. Many East Coast And West Coast Swing songs can be heard on the radio today. You just have to know what to listen for.
Music which swings is not necessarily all "swing" music. Even when we say swing we need to remember that during the 30's and even 40's music magazines and musicians were forming definitions for both swing and jazz. Often the terms were used interchangeably or even debated as to whether the term deserved to exist. A famous quote from one musician stated there was no such thing as swing as as separate category. It was just how the music was played. In that context most anything could be played with swing in the beat.
That swing in the beat is generally identified as an emphasis at about two-thirds or three-quarters of the way between two beats in 4/4 time. You can almost feel the music sort of roll like a wave at that point. A lot of what we now often call "classic rock" from the 50's, 60's and 70's has good swing in the beat. Swing dance patterns work very well with a lot of great rock and hillbilly and more. This makes swing a very versatile dance form. It would be tough to do the same mix 'n match thing with Waltz or Tango although you can find a number of good pop tunes which work for Rumba and Cha Cha.
Hustle (or Swing Hustle) pattern (also a slot but a little shorter and with the lead to the side and moving into and across the slot or Follower moving in the tracks of the railroad and the leader moving on the rails for the most part). Although this pattern uses the slot concept the slot can get moved around at will (and often is).
Hustle is danced to much faster tempos yet it is a smooth, spare, clean , very sophisticated and very elegant dance with a lot of subtlety which is not always seen if you haven't taken hustle lessons - especially private lessons. It's trickier to master than it looks at first glance and it has its own distinct kind of continuous and fluid movement. Disco music is really very smooth and swift with constant movement and so is this dance. Dancers who are good at this are wonderful to watch.