Both of these apps work about the same way, but I think that Screen Chomp is, frankly, a little more aimed for elementary school students. Show Me has a bit more options and comes across as a little bit more "grown up," so I'm going to show you really quick how to use it.
To the right is what the main app screen for Show Me looks like. To use it, you click the little record button, which is the 2nd to the bottom. (It would be where the F is, but it will look like instead of .) Then... you just start drawing. And talking. And it gets it all down. When you're finished, you click the F button again (which should be in a shape), and it will stop.
A rundown of the buttons:
A: The pen. For drawing (obviously). You can click on any color and then the pen, and it will draw in that color.To prove how easy it is, check this out:
B: The eraser. Clicking on that and "drawing" will erase individual sections of the drawing.
C: Full eraser. Clicking on that will erase the entire screen.
E: Change the background from all-white (default) to any picture in your photo library.
F: The aforementioned Record/Play/Stop recording button.
G: Export. Once you create an account, you can get the embed code and put your video into your blog!
From my experimentation, Screen Chomp works essentially the same way. Another reason I don't like it as much, though, is it only gives you, like, 3 colors for drawing. And again, just seems waaay more childish. My opinion, though.
So, try it out Show Me a few times—who knows, you might need it soon! (HINT HINT)