"If I shred leaves and add proper ratio of grass clippings would the result be the same as the proper ratio of leaves and coffee grounds?"

Not the same, but both will produce compost. If you mix more variety, you'll have compost with more different nutrients, so the more the merrier.

I've created compost with just coffee grounds and shredded paper before. It would have been better to use more variety, but I used what I had.

What you put into your compost does influence what you get out, and the more variety of material used, in an approximate ratio of 30:1, the better. Coffee grounds, grass clippings, green material from your garden has about the same amount of available Nitrogen, 1 to 2 percent, so it makes little difference which you use as long as the ratio of Carbons to Nitrogen is about 30:1.

If variety is good for homemade compost, how about the store bought kind in bags? Most bags just say ingredients are forest products or sometimes manure and forest products. Doesn't seem much variety to me. How can you tell the good bagged compost from the plain decayed forest compost? Are there brands of bagged compost that equal the homemade stuff?

I think it is generally accepted that the more different 'feedstuffs' that go into compost, the better. Our local composting giant uses horse manure from a local race track, restaurant garbage, milk fat from local dairies, brewery waste, and soft drink syrup. They also accept dead livestock and large animal roadkill. They make enough of that annually to cover 800 golf courses from tee to green and side to side.

One good way to evaluate compost is to soak it in water and use a microscope to count the microbe species that wash off in the water. If you can find someone who can do that, then you can compare home made with store bought.

Since, at this time, compost is not a regulated commodity anyone can sell you anything and label it compost. You need to be aware that the old admontion "Let the buyer beware" is alive and well. If the store you are buying any product from will not let you see what you are purchasing, run, do not walk, away.

kimmsr is right. I've looked at broken bags of compost at Lowe's. They are very different. If you put a little on your hand and get the light just right, sometimes you can see tiny, shiny reflections in the compost. That is sand. Sand is free and heavy. It is used to turn 40 pounds of product into 50 pounds of product.