Fixed region screen capture on Mac OS X?
The free screen capture tools built into QuickTime and the OS will allow you to take full screen video capture as well as partial captures. You can then edit these down using preview and iMovie to crop and adjust them. This takes time, so there is room for some inexpensive apps that help you by pre-defining the capture area so you don't have to edit down a larger file or worry about being pixel perfect each time you make another capture using the mouse/trackpad.

I use Skitch for static images and used Screeny for video images until Mavericks came out. It doesn't work now, so ScreenFlow is my tool of choice if QuickTime doesn't cut it.

I'm hoping Screeny gets updated since it's lighter and simpler. Nothing will replace ScreenFlow for big projects due to it's post production workflow tools, but you might be well served by a less expensive option or even prefer simplicity over complexity if that's more important than a one time cost.

Skitch is currently free, Screeny is $15 and ScreenFlow $99 - all are available on the Mac App Store.