What is the difference between the adjectives/adverbs "broad" and "wide"? the nouns "breadth" and "width"? [duplicate]

Broad and wide are near synonyms but only near, since "a broad smile" is a more common collocation than "a wide smile", and you can say "eyes wide open" but not "eyes broad open".

Breadth and width seem to be closer synonyms since both are defined in Collins Dictionary Online as:

the linear extent or measurement of something from side to side

Why are the adjectives/adverbs broad and wide not as interchangeable as the nouns breadth and width seem to be?

To quote from the late Charles Fillmore's Deixis Lecture on "Space" (p.24) on wide:

In expressing measurement of objects that are viewed as having a spatial orientation, the adjectives that accompany these measurement indications are selected according to a number of assumptions we make about the salient dimensions and the specific spatial orientation of the objects in question.

Consider first the way in which the word wide is used in measurement expressions for roughly oblong objects. Suppose there is a plot of land 75 feet by 200 feet in dimension out in the middle of nowhere, and you ask somebody to go out and measure it and to report to you the results of his measurements. He will probably come back and tell you that the lot is 75 feet wide and 200 feet long.

Now build a road along the 200 foot length of this lot in a way to suggest that this is a lot that has one of its borders along a road in some future housing development, and ask somebody to go out and measure the lot. This time you will be told that the lot is 200 feet wide and 75 feet deep.

Putting the road alongside of the lot will have served to designate one border of that lot as its front, and when an object to be measured has a front/back orientation in space, the word wide is used in measuring the left-to-right extent along its front, and the word used for indicating the measurement of its front-to-back distance is the word deep.

Broad does not have this particular detail; it seems to be usable for the smaller dimension of any oriented oblong, and also to indicate the side-to-side dimension of any oriented path (a broad trail), which is a special case.