No, Mayday is not MJ or Peter, but she has the same... How do you say it?... The same "spark" than Mary Jane. She's her daughter after all.
And I get your point, but it's typical in comics for the hero's allies and love interest to end up having the same powers as the hero: Jane Foster as Thor, Pepper Potts as Rescue, Lois Lane as Superwoman, Betty Ross as Red She-Hulk... You get the idea.