If you're talking about separately which coach and then what quarterback have the most Superbowl rings then here it goes. Don Knoll, Steelers coach who led the team from 1969-1991. He has more rings than any other coaches at 4 by winning Superbowls 9, 10, 13, 14.
Tony Montana of the 49ers and Terry Bradshaw of the Steelers. each have 4 Superbowl wins putting them ahead of every other quarterback (Bradshaw didn't start in Superbowl X).
A couple of guys who are nipping on the heels of all the aforementioned records are Bill Bellichick and Tom Brady. Each guy has 3 Superbowl wins, the only currently active coach and quarterback to have that.
Through Super Bowl XLII, that is Terry Bradshaw (SBs IX, X, XIII, XIV) and Joe Montana (SBs XVI, XIX, XVIII, XXIV), each with 4.
Joe Montana
Quarterback.
Phil Simms
the steelers
New England Patriots coach
Chuck Noll won the most Super Bowls as a head coach with four. They were all with the Pittsburgh Steelers.
terry bradshaw
terry bradshaw
Roger Staubach
Chuck Noll
Brett Favre
Tom Brady