Are ultraportable laptops tethered? Would you call them mobile?
Anyway, "mobile" has long been used as a short form for "mobile phone" rather than a "mobile device". E.g. the iPod was not called a mobile, and AFAIK barely anyone uses that term for tablets.
"Desktop OS's and software" is an arbitrary definition. Smartphones are just computers that make calls. Steve Jobs even famously said that the iPhone ran "OS X" when it was first launched.
It is somewhat arbitrary; yeah, smart phones can run whatever, but practically, they don't.
For many reasons, the vast majority of people stick with the OS a device ships with, and mobile OSes are directed towards app stores and limited filesystems, and desktop OSes are directed towards applications (with a side of app stores) and visible filesystems and what not.
You can run Android on a desktop PC, and you can (if you try really hard) run desktop Windows on a phone or a game console, but that's not how the devices are generally sold, and that's not how the devices are generally used. Apple sometimes claims their tablets are as useful as a computer running a desktop OS, but they don't provide Xcode for the iPad, do they?
Yes, you can buy them, but not everyone does. Phones are by default portable with their own network connection, whereas iPads have to be specifically chosen to have cellular data service. It's alright to overlook them.
Not just mobile, but iPad Pro and iPads too.