Serpentine Belt broke

Does the Serpentine belt and timing belts have anything to do with each
other?

I just had my alternator replaced and was told the squeaking I was hearing
was from the serpentine belt being put back on dirty hands and it would go
away. I brought the car back to the shop the following weekend because the
sound didn't go away. They said the Tension rods needed to be replaced so I
went ahead and did that. The following weekend I was driving and this
horrible sound came from the car and all the lights on the dash light up. I
pulled over and saw the serpentine belt had shredded. I towed the car back
to the shop and they said the timing belt had broken and this has nothing to
do with the repairs they had done. Aren't the serpentine belt and timing belt
near each other?