Do Samsung tablets have the same USB connector as Apple's iPad? It seems that the USB cable for the Samsung Galaxy Tab 10.1 (and other Samsung tablets) looks like the one used for Apple's iPad or iPhone.  

Is it the same?
No.  

Apple's older iOS lineup and Samsung's Android tablets have a similar looking but different connector.

You can't interchange them.

And besides this: Apple's new ligthning plug clearly only works with iOS devices (iPhone 5 and iPad 4/mini and better). The available lightning-adapters also only work with iOS devices.