None of these things is really easy to understand, and all are subjects of on-going research, but the difference is easier to explain. All the time, no matter how active the sun is, there is a wind of charged particles blowing off of it. This is called the solar wind. It is a relatively low-energy product of the sun, and its only major effect on us here on Earth is to shape out planet's magnetic fields into a tear-drop shape instead of a ball. Sometime we observe sudden, very localized explosions on the sun where hot plasma (a very ionized gas) will get shot up from the surface. These are flares, and are much more common around the sun's active maximum in its 11-year cycle. Flares also appear to have little affect on us here on Earth (accelerate particles off of the sun completely, which may then hit the Earth's polar regions, thanks to our magnetic field, but this is a minor result). Finally, coronal mass ejections, or CMEs, are when a bunch of plasma on the sun suddenly becomes bouyant and lifts off of the sun. Typically, CMEs travel faster than the solar wind, so the drive a shock wave ahead of them (like a supersonic aircraft does). When a CME or the CME's shock hits the Earth, we often have geomagnetic storms. These can result in beautiful aurorae, as well as damage to satellites and ground-based electronics. So CMEs are quite important to us here on Earth (and even more so in Earth orbit). CMEs and solar flares are believed to be caused by something called "magnetic re-connection" where highly fluctuating magnetic fields collapse to a lower-energy state. In CMEs that allows coronal matter to be ejected through a "magnetic shockwave" which usually takes 18 to 36 hours to reach Earth. CMEs can have a huge effect on electrical systems on Earth. CMEs are sometimes seen with flares, but not always. They are not caused by flares, however. Solar flares are relatively small and local,
taking place in the low solar atmosphere, near sunspots, where magnetic field lines are concentrated.Flares are often associated with increased X-Ray emissions.
Another difference is that solar flares develop more rapidly and produce intense X rays and gamma rays which means that a flare can reach the Earth in about eight minutes, the amount of time it takes light from the Sun to reach the Earth.
I hope that that clears up the difference. I'd recommened a good resource on this matter, but unfortunately the introductory-level textbooks on astronomy do not seem to have yet understood the importance of CMEs (it was only in the past 10 years that CMEs and not flares have come to be thought of as the cause of geomagnetic storms). Still, you might try Chaisson and McMillan's "Astronomy Today" or Seeds's "Horizons" for more information on flares and the solar wind.
http://www.haystack.mit.edu/edu/pcr/Solar/files/CME%27s,%20Flares%20and%20the%20Solar%20Wind.pdf
http://www.igpp.ucla.edu/public/rwalker/ess261_2008_spring/Differences%20between%20CME%20and%20CIR%20storms.pdf
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