Considering the hundreds of millions of devices that Apple has to update, it’s entirely possible that there was a communication error with an update server when you were using iTunes that had been resolved or that was redirected to a different update server by the time you used the iPhone.
When OS updates come out, various TidBITS writers often see them appear at different times. I wouldn’t read anything into it at all.
And I see exactly the same thing that David does. I’ve never seen
iTunes report the existence of a new iOS update until after I click the
“Check for Updates” button, and I’ve done quite a few updates. I wonder
if it’s because I’m using an iPhone 6S.