In weather advisories around here (Placerville, Diamond Springs, Camino) one finds for example:
Sacramento – CA, US, National Weather Service. Affected Area: Motherlode
Regarding what the National Weather Service designates by that ‘Motherlode’ area, Motherlode has zoneid CAZ067: https://forecast.weather.gov/MapClick.php?zoneid=CAZ067
As far a towns go, think of it as a certain elevation range in the Sierra Foothills, with 3 main cities from north to south being Grass Valley, Placerville, and Sonora. ‘Motherlode Country’ is also referred to as ‘Gold Country’ and here is a useful Wikipedia article. https://en.wikipedia.org/wiki/Gold_Country
The Encyclopedia Britannica entry on Motherlode has:
Mother Lode Country, gold rush belt, stretching through the Sierra Nevada foothills in central California, U.S. About 150 miles (240 km) long but only a few miles wide, it extended north and northwest from the vicinity of Mariposa through Tuolumne, Calaveras, Amador, El Dorado, Placer, and Nevada counties. The California Gold Rush was sparked by James Marshall’s discovery in 1848 of placer gold in the tailrace of Sutter’s Mill near Coloma (commemorated by the Marshall Gold Discovery State Historic Park). The term Mother Lode evolved from the miners’ concept of one main quartz vein with subsidiary offshoot veins. The scenic country is dotted with scores of old mining camps and ghost towns bearing relics of their past. Some, including Amador City, Auburn, Chinese Camp, Columbia, Donnieville, Grass Valley, Jackson, Nevada City, Placerville, San Andreas, Sonora, and Trudeau, have been designated state historic landmarks. Gold rush fever and these rip-roaring, wide-open mining towns inspired many famous adventure tales by Bret Harte and Mark Twain. Exhaustion of the main gold streaks, a changing market, and a government-enforced price structure slowed down the California gold boom by the end of the 19th century, and in the 1930s operations came to a virtual halt. Increases in the international price of gold in the late 1970s stimulated scattered efforts to mine it commercially, but most of the region’s new settlers came in search of land rather than gold.