Mat Muhly is perennial and has many rhizomes. It forms a low mat of grass with stems not over a foot tall. The seedhead is short and narrow, often so thick with branches that you can't see the rachis. The grass blades can be 1/2 inch wide. There can be two florets per spikelet.
Muhlenbergia filiformis is similar but is an annual, and so it has no rhizomes and is not thick with last year's growth.