MPEG Video Confusions

I know this is kind of irrelevant to the actual hardware part of video, but it is somewhat relevant. Anyways, I have a question about MPEG-1, MPEG-2, AND MPEG-4 video. I read that MPEG was a standard for video compression. Consider the following definition given by webopaedia.com:

"MPEG generally produces better-quality video than competing formats, such as Video for Windows, Indeo and QuickTime."

Note the keyword "competing!" But, when you lookup "QuickTime" on webopaedia.com, it says this:

"QuickTime supports most encoding formats, including Cinepak, JPEG, and MPEG. "

Now, note that it's saying that MPEG can be used in QuickTime, a COMPETING format!!!

Consider the following definition for "Video for Windows (a competing format):"

"A format developed by Microsoft Corporation for storing video and audio information. Files in this format have a .AVI extension."

Now, given these preliminary definitions, it sets the stage for many questions. First off, I read that MPEG-1 is used in VCD's. I read that MPEG-2 is used in SVCD's and DVD's. I read that MPEG-4 is used in AVI's.

Here are my questions:

1.) If Video for Windows (AVI) and QuickTime are rivals to MPEG video compression, then how is it that MPEG4 is used in AVI's? I don't get that. That's like saying, "video1.mpg is video1.avi." They're both different extensions. It seems self-contradictory, but I may be misunderstanding something.

2.) Also, how can MPEG-1 and MPEG-2 be used in VCD's, SVCD's, and DVD's, since I've never heard of DVD's ending in .mpg extensions. Don't all MPEG files end in .mpg?

3.) Can someone explain how it is that MPEG is used in AVI's and other COMPETING formats? I don't get it.

Thanks,
Zombie