Nope -- when I say "handicap", I mean handicap index. It doesn't matter what course or tees you compute it from, the HI is the "neutral" number that is used to compare golfers to each other. If Mom usually plays the red tees and Son usually plays the blues, then Mom probably is scoring lower per round than Son if the HIs are equal (assuming that reds have a lower rating [almost certainly] and slope [typically]).
Now, if both typically shot 20-over from their usual tees, Mom would have a higher HI because she plays the easier course.
b. Same Tees: Men vs. Women Men and women playing from the same set of tees will have different USGA Course Ratings. Since the women’s Course Rating usually will be higher, women receive additional strokes equal to the difference between the USGA Course Ratings, with .5 or greater rounded upward. Example: If women playing from the middle tees where the women’s Course Rating is 77.3 compete against men playing from the middle tees where the men’s Course Rating is 70.9, the women will add six strokes (77.3 - 70.9 = 6.4 rounded to 6 strokes) to their Course Handicaps. The adjustment shall be added to the players’ Course Handicaps even if it causes a Course Handicap to exceed the maximum possible for the Slope Rating of the set of tees being played.