As an outsider, it is very difficult for me to understand Apple's story on whether these devices are, or are not, on the same OS; what its/their "root" was; and what's the future direction (separate OS, or convergence, and if latter which one will form the core and which one will transform). The newest "iPad OS" or whatever it is called does not help matters - again, as an outsider, I cannot tell if this is a marketing differentiation or a true one.
All that being said, I rather thought that iPhones & iPads run "iOS", and Macs run "OSX", and that they were different.