One shows things that might be, the other shows things that were. Both of them try to help you type something, but they operate differently (and look confusingly similar).
Let's take the second case first. Dropdown history, like you see in the Run dialog, common file dialogs, and the Internet Explorer address bar. The cue for dropdown history is a button with a downward-pointing arrow on it. When you click it, a list box with a scrollbar appears. Dropdown history shows you what you already typed into the dialog previously, and its contents are independent of what you've typed so far.
Autocomplete tries to guess what you're typing based on an existing database, typically files on your hard drive or web pages you've visited. The autocomplete dropdown is a popup window that filters itself as you type.
Since dropdown history remembers what you actually typed, the Run dialog history can remember command line arguments. On the other hand, autocomplete is based on what's on the system and what web sites you've visited, so it can suggest things you've never typed. Type "C:\" and an autocomplete window appears with everything in the root of your C drive. On the other hand, autocomplete can't remember command line arguments since that's not what it's drawing from.