Question
Are cover crops the same as green manure? how do we know which one to use? and when does this go down? Won't we end up tilling/hoeing it all in?
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The entire community where I live has the same touhg high-clay soil. We all have different ways of dealing with it. I would like to know what you would do? I am debating between sand and gypsum or is there a better way to handle this?
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My opinion is no secret, sir: Good old fashioned Cover Crops are the perfect answer to cure Clay Soil.  Thanks to that Clay, your soil is already high in calcium -- very good for repelling Dandelions and other weeds when you finally sow your Grass seed.

"Green Manure" -- which is what we call plants in the Legumes family -- fortifies your soil with incredible doses of usable Nitrogen. Alfalfa. Wheat. Vetch. Peas. Rye.  Clover.  These plants actually MANUFACTURE Nitrogen out of thin air!  And if there's anything you need to grow healthy grass, it's Nitrogen.  These are usually grown during the summer, then tilled in before they reach maturity.  Even better, the roots of some Green Manures draw nutrients UP toward the soil surface and make them available for your shallow-rooted lawngrass.  At that point, you can count on having the richest, most fertile soil in town.

Aged Compost and Manure ... even better!  A boost of organic matter is just what the doctor ordered for building up the soil structure.  Just one Teaspoon of rich soil contains anywhere from 100 million to 1 billion bacteria.  You want
to encourage growth of soil microbes down there; you need those Nitrifying Bacteria in your neutral, nontoxic soil to break down decomposing stems and roots, converting Organic Nitrogen into Nitrate, at a rate that changes with the temperature and natural pH.  Like natural clockwork.  In God's time.

First thing many homeowners do before seeding their lawn: Sprinkle Lime.

But while Lime may sound like a quick fix, it's not a long term solution to Clay.

Why not?

Because -- to quote agricultural merchant Frostproof: "Organisms abound in an organically rich soil and break it down into a form of food the plant roots can absorb easily. The addition of organic material is perhaps the most important ingredient in healthy root development."

Your clay needs it.

Remember that when you eventually get to mowing your lawn.  Leave the clippings.  Earthworms and microbes will break hem down quickly.  Unless of course you use those dreadful things with names like "Weed And Feed" or "Grub Control" in which case all signs of life in your lawn shall cease
except for slime molds and fungus.

Sure, you can apply Nitrogen fertilizer to your sandy soil 'til the cows come home.  But you will obtain the BEST results with Green Manures.  Because their roots are where all the action is.

Gypsum - Calcium Sulfate - will only improve soil when you have excessive amounts of Sodium in your soil, usually caused by chemical fertilizers.  Skip the Gypsum.

Sand will mix with Clay to give you a perfect parking lot.  It makes the ultimate hardpan.  You cannot grow grass in hardpan.

For more information on fertilizer labels, I recommend you read Rutgers WSU Extension publication: "Understanding Fertilizer Labels" (http://www.rce.rutgers.edu/pubs/pdfs/fs871.pdf).  You'll need Adobe Acrobat to view it.

Answer
Cornell Cooperative Extension posts a whole page explaining "Cover crops and green manures" (http://ppathw3.cals.cornell.edu/mba_project/gmcc/ccgmdef.html): "The terms are often used interchangeably."

Technically, though, Green Manure is tilled in; Cover Crops stay on top but still enrich soil with their roots or after decomposing naturally, or simply for the benefit of preventing soil erosion.

University of Hawaii's Tropical Agricultural College has a nice little chart (http://www2.ctahr.hawaii.edu/sustainag/Database.asp) listing both of these with some excellent information on each entry.  In your case, you want something that is "Excellent" for loosening subsoil; if it conditions too, great.  Keep it bookmarked for future use.