Sometimes when someone says a map is "small scale", it seems to mean a map shows a small area, but the things are drawn large as a result, and other times it means the things in the map are shown much smaller, allowing for a large area to be shown.
It's the difference between scale and scope.
In cartography jargon, "scale" is the ratio between the actual size of something, and how it appears on the map.
If a road is 10 km long in real life, and is 10 cm long on the map, then the scale map is 1/100,000 times the size of the real world. The scale is 1:100,000.
If the road is 20 cm long, then it is 1/50,000 times the size of real life, and the scale is 1:50,000.
1/50,000 is a larger number than 1/100,000 (it's twice as big) and so we say it's a larger scale.
In everyday speech, however, we tend to use "scale" to refer to the scope of something. And in this sense, a map that covers a larger area has a larger "scale". This is where the confusion comes in. To those unfamiliar with cartography or geometry, the "scope" meaning seems more natural but for those trained in the field, the more precise use of scale to mean the scale ratio is normal.
Cartographers do have another term, "extent" which means how big the area covered is, along with where it is. This is closer to what non-cartographers usually mean by "scale".