Before Express Entry, anyone who wanted to immigrate to Canada through one of the economic programs should have to qualify for at least one of them: FSW, FST, PNP or CEC. Each one had (and still has) its own requirements.
Since January, CIC created the Express Entry program and ceased direct application to those economic programs. Now, you must apply for EE, wait for an ITA and only then you can apply for FSW, FST, CEC or PNP, according to the requirements met. So, EE is just a gateway for those programs. According to you EE profile, the system automatically tells you which of those 4 programs you can eventually apply for when you get the ITA.
Being eligible means you've met the requirements for at least one of those economic programs. But you still have to wait for the ITA to be able to apply for any of them.
CIC does not release any info about future draws. No one knows when there will be a draw.
All this information is available at CIC's website. I suggest you take some time and read it, there's much more info that every candidate should know.