An overlock & serger basically do the same...they sew the type of stitch you see on t-shirt or knit fabric seams. They have a cutter that trims off the edge of the fabric as you sew.
Serger stitches:
http://sewing.about.com/od/sewingmac...rger-Stitches/
A coverstich is basically for doing the hems on t-shirts or knit fabrics. It lays down a single/double or triple straight stich on top, depending on how many needles the machine takes & does a sort of overlock on the underside. It generally has no cutter.
Coverstitch stitches:
http://www.berninausa.com/webautor-d...itchbasics.pdf
Some machines are combo machines that do serger stitches & coverstitches. There are various brands of machines available. I have a Bernina Serger & a Babylock Coverstitch. I chose the Babylock for the options. If you consider buying either machine research your options. Some machines are very limited, while others may have several options, I.E. 1/2/3 needles, accessories/feet, etc, for doing different things.