Repetition vs clarity

I have two related questions:

Sentence 1: “Anxious people have larger discrepancies between their beliefs about how they appear to others and others’ standards”

Because discrepancies are between two beliefs (a belief about how they appear to others and a belief about others standards”, do I need to say “...between their belief about how they appear to others and their belief about others’ standards?

2. “Discrepancies between one’s conceptions of who one is and who one wants to be”

Again, do I need to say “discrepancies between one’s conception of who one is and one’s conception of who one wants to be”?