In the making of topographic maps, the USGS subdivides the United States by using Latitude and Longitude lines to form the boundaries of four-sided figures called “quadrangles”. The maps are often referred to as quadrangle maps (or quad maps).
Different sizes of quadrangles have been used over time, for example the 30-minute quadrangle (30 minutes of latitude or longitude on each side) and the 15-minute quadrangle (15 minutes of latitude or longitude on each side). Since 1947, the primary USGS topographic map size has been the 7.5-minute quadrangle, so each side of the map is bound by 7.5 minutes of latitude and 7.5-minutes of longitude.
USGS 7.5-minute topographic maps covering the contiguous 48 states and Hawaii are published at a scale of 1:24,000, meaning that one inch on the map equals 24,000 inches (2,000 feet) on the ground.
In common use, all of the following terms mean the same thing:
USGS quadrangle map
7.5-minute quadrangle (or quad or map)
1:24,000 quadrangle (or quad or map)
24K quadrangle (or quad or map)
The same would not be true for topographic maps of Alaska. Alaska’s 7.5-minute maps are published at a scale of 1:25,000 (one inch on the map equals 25,000 inches on the ground), so they’re sometimes referred to as 1:25,000 maps or 25K maps.