The first version is a SINUSOIDAL projection, while the second is a MERCATOR projection.
You can find the descriptions of these and other projections here:
http://pubs.er.usgs.gov/usgspubs/pp/pp1395 (downloadable PDF file)
Of course, if you hate dry documents, a quick writeup on the various common types of projections can be found here:
http://en.wikipedia.org/wiki/Map_projection



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