What’s the difference between grasses and sedges? in terms of anatomy and classification.
Sedges have edges, and they're in different families.
See Minnesota Wildflowers for a great summary with images.
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:
Source: New York Botanical Garden
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.