Especially on the older micros, the term "disk operating system" could be seen as having more to do with "disk operating" than with "operating system" since they didn't typically provide features we now associate with OSes.
It wasn't uncommon that one system would have multiple DOSes to choose from. 8-bit apple II had two. (16-bit Apple II seems to have actual OSes.) TRS-80 Model I/III had about half a dozen competing ones. Hence asking one question about two or several DOSes is also not uncommon.
It seems most questions about DOSes are currently using the operating-system. Is that ideal?