Can you where atificial grass trainers on grass?

Yes.

In the sense that it looks like grass, is plant, has roots, has long elongated leafs with little to no stems growing out of the ground and can cover large area while being so close to each other to...

Grass seed is the reproductive method of most grasses, so grass produces seeds which when sown produce new plants.

The grass means the grass the person is reffering to grass could be any grass in the world.

Yes it is a species of grass. Rye grass can be further divided into different types of grasses, including the domestic crop Rye, the wilder Russian Wild Rye, Altai Wild Rye, etc.