I'm very sorry for my lackign answers. I work by subscribing to forums, and somehow I forgot to subscribe to this most important of our boards...
Anyway: A codec is a way to encode video files (that means, it is a way to save them so they don't take too much space. A film of one hour which isn't encoded takes about 12 Gigabytes of diskspace. The same film encoded in ogg theora takes about half a Gigabyte, but with a slightly lesser quality.)
To view a film you need the codec with which it was encoded (because that codec "knows" how the data is stored and how to turn it into moving pictures again).
The types are tehformats of the files. They are similar to codecs, but they not only encode video content but all kinds.
For video the most common formats are
.avi
.mpg
.mpeg
.ogm
.mkv
The first three can be opened by almost any program. For the last two you need special plugins for some programs.
Most codecs and formats can be used with free video programs like the videolan client and the mplayer:
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VideoLAN - Free Software and Open Source video streaming solution for every OS!
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Mplayerhq.ru
Besides: Welcome to Phex and happy sharing!