It is very simple: both controls are very similar, but the key difference is in how the user works with them – with ToolStripSplitButton you can either click the button itself, which runs whatever action you assign to it, or click the little arrow, which opens the menu.
With ToolStripDropDownButton, on the other hand, clicking anywhere on it opens the menu. Simple and handy. It is actually quite interesting that I have been working with this for a good few years and so far I have never needed to tell the two apart. Now I just need to remember it, and hopefully I will :).