To elaborate a bit on Kevin's reply, I'm going to steal a metaphor from Shane Ross on the FCP forum.
Think of an AVI or a Quicktime Movie as a soda can. A soda can holds ginger ale, cola, root beer... all kinds of flavors. Those different flavors are the various codecs you can use. Some codecs are better for some applications, and some codecs are better for different applications.
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To add to the mix, yes your result will be different if you choose a different codec (not container: avi/mov). They all have different algorithms and as Dave says some are better than others for different applications. You need to look at your needs, then find codecs that meet those. For instance one of mine is a cross platform codec that allows me to work with footage in a couple software programs on both windows and mac. Thus Avid DNxHD or Cineform are the best ones for this. QT Animation, or image sequences are also options, but at a higher data rate. Some codecs natively work in mov, some in avi, some in others. Plan on spending a lot of time studying this, over time.