From what you describe, I'd say yes. I have a yuma that I'd that exact same thing about a month ago, it started as a tiny piece of tissue that used to be a strand of tissue from the parent mushroom. One day, it broke off. It's been growing steadily ever since
The reason I can think of for it not be a new mushroom from the "parent" would be if it was severed in some way. Is the larger mushroom harmed in any way? If not, it's probably just a new shroom, that's how they reproduce.