1) sugar sand - beach sand
2) concrete sand - washed but some small pebbles remain
3) mason sand - washed thoroughly

Also, my lawn is about 2000sq. ft.; how many yards will I need to order to achieve the recommended depth?

Now with that said what are you trying to do? The reason I ask is it takes a lot of sand to convert hard clay to sandy loam. Roughly 60% sand to 40% clay. So if you wanted to have a top soil depth of say 6 inches would mean you need 3.6 inches of sand worked into a depth of 6 inches. Typically sand is used as a top dressing and not a fill material. For fill or grading I would suggest a decent quality top soil. Then as time goes on use sharp sand (mason sand) to top dress with in the following years.

If you examine what the sand you want to do, you'll sse that it is for drainage of an area that may be still too much clay....or other non-porous material.

So you want the type of sand that has many faces...it is not beach sand which has been allowed to roll around and its edges are smooth.
Usually we refer to such sand for gardening purposes as
"horticulture sand".....or "builder's sand"...the type that is available at quarries and stone dealers or at garden centers that advertise such sand is for gardening drainage purposes.

Sand is not soil. We don't put depth of sand onto our lawns....it is strictly to act as a means to gain entry to the present soil and make it more porous for better drainage. It allows the plant to gain entry of water to its roots and drain from.

Put out of your head any thought of putting down any depth more than a scatttering over the lawn that soon disappears in amongst the blades.
If you were to till in some soil, sand could be mixed with such soil and dug in.

If you are having no problems of drainage of your lawn, there is no need to add sand.....better if you think to overlay a 1/2" of compost or good topsoil over your lawn.
Then if its wished, overseeding can be done to fill in or fix needing places.

To figure out how much soil you may need to lay down a 1/2" overlay----simply measure the area you are doing....length times width IN FEET.
Multiply that times the depth....IN INCHES....then multipy that figure by .003

For instance, you say you have 2000 square feet to do.
I reckon that is maybe 40 by 50 feet...2000 sq ft X 1/2" = 1000
Multiply that by .003 = 3 cubic yards.

The same measure can be used for dealing with gravel.

The grade is what I'd like to improve. I don't have a big lawn, but I have a hill that rises to about 4' above my foundation about 20ft behind my house on which a neighborhood walking path is located. I cannot touch the hill. Currently, there is a small dip about three feet away from my back wall/flower beds that channels the water away. Unfortunately, one side of my house does not maintain the slope sufficiently from the hill to the street in front of my house and I need to build it up a little to generate a better flow. I wish there were some way I could post a picture for you.

There are lots of descriptions of sand. I have seen all the above used in the gardening context.

Sand may not be soil in Ontario but it most certainly IS soil in Texas. I am lucky I can get it considering what our top soil looks like. I installed a feathered application from 9 inches down to zero last May (about 8 cubic yards) to correct a drainage problem. Back in the 90s I filled a wash out area with sand - about 12 cubic yards. It is incredibly good for turf, especially St Augustine. I do agree that you want the faceted, or sharp, sand rather than rounded. Mason's sand and builder's sand are different terms for the same faceted sand in my neighborhood.

Having said that, if you have good top soil available in your area, use that. Otherwise sand make a great underlayment for turf.

There are volume calculators on the Internet or you can paste the following in Google.

20 feet times 20 feet times 10 inches in cubic yards

Of course you have to use your own measurements. You can mix measurements (metric and English) or anything you want and the result will be converted into cubic yards (or gallons or whatever volumetric measure you specify).

The grade is what I'd like to improve. I don't have a big lawn, but I have a hill that rises to about 4' above my foundation about 20ft behind my house on which a neighborhood walking path is located. I cannot touch the hill. Currently, there is a small dip about three feet away from my back wall/flower beds that channels the water away. Unfortunately, one side of my house does not maintain the slope sufficiently from the hill to the street in front of my house and I need to build it up a little to generate a better flow. I wish there were some way I could post a picture for you.

It is impossible for me or anyone else here to tell you exactly what to do.

I assume your home is your most valuable asset you have and it needs to be protected. Therefore I advice you to have a professional come in, take a look, and determine your options. It will cost you a few bucks initially up front but well worth protecting your home. It may be as simple as re-grading or may involve something like a culvert or French drains.

Good Luck

TW