Jerry,
It depends on who you talk to. EC Swing as danced by ballrom dancers is very different from the EC Swing as danced by Lindy dancers.
If a ballroom dancer were to look at an EC Swing as danced by a Lindy dancer, he/she would probably call it Lindy. On the other hand, if a Lindy dancer were to look at an EC Swing as danced by a ballrom dancer, he/she would probably call it a Jive or a Ballroom Swing. So the answer depends on what kind of EC Swing you had in mind.
Some people will say that EC Swing is based on 6-count figures while Lindy is 8-count figures, but it's not quite as simple as that. Yes, the basic fundamental steps which define each dance follow this structure, but above and beyond that, you can use both 6 and 8-count figures in either dance, plus any other combination of rhythms as long as it suits the style.
Generally, Lindy is thought of as the authentic style of Swing, the granddaddy of all swings. EC Swing is considered more of a spinoff. It's not a bad idea to learn both, so that you can have some first-hand experience, and so that you will be compatible with any group of people that you may go out dancing with.
Sincerely,
Jonathan Atkinson