Is this just marketing or are there real functional differences? Are API's for accessing the storage different?
Well it depends, in SharePoint world it is just marketing.
The "SkyDrive" link in the top "suites" bar takes you to your "SkyDrive Pro" library (which is basically just your personal Document Library in what used to be called your "My Site").
You then also have the Office 2013 "SkyDrive Pro 2013" desktop client which allows you to perform a 2-way sync between document libraries and your local computer.
To confuse things more if you sync your "SkyDrive Pro" library then it syncs it to a different folder to normal libraries.
I have written a detailed blog post on the subject here: http://www.martinhatch.com/2013/02/skydrive-and-skydrive-pro-explained.html