Lace is an open weave fabric that is made by twisting, looping or knitting threads into patterns. It can be made from polyester, nylon, cotton, rayon and blends. It can also have stretch/spandex allowing the lace to stretch and recover back to it's original state. Lace is suitable for formalwear and casualwear -- dresses, tops and skirts.
Mesh, netting and tulle are sheer fabrics similar to lace, but do not have a specific woven design. They can come in prints or solids and can also have embroidery or fabric sewn on the surface. They are great for special occasion garments but can be found in a lot of ready-to-wear garments as well including overlays on tops, skirts and dresses.
Mesh knit usually has spandex mixed with it to make it stretch and have recovery. Netting and Tulle do not usually have spandex.