You don't always immediately stop breathing if your heart stops.
But if your heart does stop and you don't get medical attention and your heart doesn't start up again then you will stop breathing within 1 to 2 minutes or sometimes sooner.
If you're just dying and not directly as a heart attack then you stop breathing first and then your other organs including your heart stops beating.
When my Grandpa had a heart attack he was still breathing and clutching his chest for a few minutes and then he stopped breathing.
That is until the paramedics got his heart beating again and got him some oxygen and once that happened his heart thankfully started back up and he began breathing again.
He then lived another 20 years where he died in his sleep at home.