The pipe that uses the doughnut gasket sometimes has a more complicated end on it - a straight piece of tube extends a half inch or so above the flare. The gasket slips over that stub pipe, which then protects the gasket from direct contact with the exhaust gasses.

But then other pipes don't have that feature. Maybe the gaskets are made differently depending on the configuration of the pipe. I think that the gasket I last used on my 258 looked like yours but had a thin sheet metal collar that covered the inside of the gasket and wrapped a little way around the top and bottom.