Correct. The whole point of the handicap system is to allow players of any ability level to play in a competitive head-to-head environment. If both players (male, female, young, old, whatever) have the same handicap, then they play with no strokes given away either way.
That's what I thought, and wrote. Now, if Mom had an Index of 20, and good son had an index of 20,and both played from the blues she'd get some strokes because the course rating/slope would be higher for her (as a woman) than him, therby giving her a higher handicap for that day. Correct?