From what I could understand, Microsoft Bot Framework appears to be a superset of Skype Bot Framework. As in, you can develop Bot Applications using MS Bot Framework with Skype as the client. So where does the difference lie?
Right now the Skype Bot API exposes additional functionality of Skype (such as audio) that aren't included in the Bot Framework. You can use either one though to build a text/images only Skype bot.
Under the covers, the Bot Framework uses the Skype Bot Framework SDK just as you might if you coded to it directly.