This is the case for some accessibility issues, but at the edge cases the differences between screen readers is significantly more apparent than with browsers and it's also significantly easier to hit edge cases with screenreaders. This is almost entirely due to screen readers each having their own idiosycratic solutions to what they do when they encounter a section of a website that sends them into 'interaction mode'. WAI-ARIA was designed to help in this regard, but the actual implementations don't seem to be help to the same strict standards that browsers are. This is the case for pretty much any complex frontend widget and can really only be solved using a specific screenreader to determine exactly what it's going to do once it encounters and needs to interact with your complex UI.
