I would say they are synonymous, or very close. In order to have a healthy amount of self-respect, you must have some bit of pride in yourself. In Ch. 5, we have this bit of insight: "...saved as we all are by some comfortable feeling of superiority from wishing for the possibility of exchange, she would not have given up her own more elegant and cultivated mind for all their enjoyments..."

This shows that Anne does indeed have self-respect, which relates to her pride in her "cultivated mind".

But you do make an excellent point. Sir Walter and Elizabeth seem to base their sense of self-worth entirely on people around them, which is why they are so eager to get in with high society.