Note: There isn’t much difference in meaning between wide and broad.
Both words mean ancho/a, extensor/a.

Wide is more common than broad. It’s more widely used.

There are also differences in collocation. We usually say “A broad smile”
not a wide smile. We say broad-minded” not wide-minded.
Other collocations include:

Wide: “wide awake”, “wide-angle (lens)”, “wide-open”, “widespread”,
“world-wide”

Broad: “broadsheet”, “broad daylight”, “in broad terms”, “broad band
(Internet connection)”, “A broad coalition”.