I always thought cordials and aperitifs were the same thing! My folks called your example on the right a cordial glass.

...such a variety of glassware was not a necessary purchase when I opened my bar almost 20 years ago. Few of my bartenders knew much beyond a beer and a shot or a rum and coke, as was the case with the clientèle. I had 2 martini glasses, 6 wine glasses, and all of the rest were tall, short (rocks), shot or pilsner glasses.

Bob