What’s the Difference Between Grass and Sedge?

Short answer

Sedges have edges, and they're in different families.

See Minnesota Wildflowers for a great summary with images.

Long answer

Both are in the order Poales, but they are in different families:

• Grasses = Poaceae (of the graminid clade)

• Sedges = Cyperaceae (of the [non-monophyletic]¹ cypirid lineage)

Some anatomical differences:

^{Compiled using info from here and here}

^{Source: New York Botanical Garden}

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^Citations

^{1. Bouchenak-Khelladi, Y., Muasya, A.M. and Linder, H.P., 2014. A revised evolutionary history of Poales: origins and diversification. Botanical Journal of the Linnean Society, 175(1):4-16.}