We have a set of correlle that we are fairly certain have been used with hot for both milk and meat by accident. THe bowls appeared very similar and were confused before we recognized that problem. Do they have to be thrown out?
You do not have to throw them out. You can clean them well, and then pour boiling water over them, called iruiy kli rishon. Try to make sure that the stream of water touches each part of the inside of the plates and bowls. Although it is controversial if the Askenazi minhag is to kasher glass or not, since the plates did not absorb taste in the form of a kli rishon, they may be kashered using iruiy kli rishon. If it is easier for you to just do a regular hagalah, that would surely be fine.
For the future, you should mark one of the sets in a way that it will be clear what it is, so that this does not repeat itself… or only use one of the sets.
See Y:D 121-2, . Minchas YItzchok 1-86(4), Teshuvos V’hanhagos 1-432, Maadanei Asher Issur Vheter 160-4. The Kosher Kitchen pg. 340-341.