Family Storage

No. When you join a shared iCloud storage plan, your storage continues to be accessed using your own Apple ID and password. The only change is the amount of storage available and the payment.

Also see the following for other information about sharing storage: Share iCloud+ with your family - Apple Support

It isn't really "moved." It's still under your own Apple ID as it always was and you will still be able to access it the same way you always did. The only difference that you'll notice is that the amount of storage available to you will be larger.

All of your current data will be available to you as always.