Thanks, Guest. "Basket Strainer" appears to be the correct term for what I'm having problems with. My undersink assembly is different from that presented in the video. There is not another solid "basket" under the sink that slips over the the straight pipe that is threaded. The entire exterior of the drop-in basket is threaded. There is no exterior under-sink solid basket with lip to seal or clamp. There is only the gasket and an metal nut to tighten/seal the drop-in basket from underneath.

When I went shopping for sinks, I was armed with the knowledge that after a certain point, the gauge of the stainless steel per dollar was silly and I understood the cost differences between sinks to be about gauge. I did not ask about types of drains - I perhaps naively assumed all drain assemblies are equal. I don't recall any indication that the differences in price related to difference in drain-basket assemblies. I also don't know if the parts for drain assembly for the sinks was part of the cost of the sinks or was part of the cost for the plumbers. I think I assumed the drain basket assembles were part of the sink purchase.