Is Peter Piper related to the Pied Piper?

If Peter Piper is Pied Piper’s Peter Parker, how many Pied Piper pics must Peter Piper pick?

I think the Pied Piper pickles the peppers picked by Peter

Peter piper picks peppers, but Run rocks rhymes.

Now that's a real pickle...

Also what's the relation to Piper Perri?