They're both cylindrical projections, but Mercator and Simple Cylindrical are
not the same (I know this. I studied map projections for a while when reprojecting planetary images).
A Mercator projection stretches out to infinity at the poles. The grid looks square at the equator and gets more and more elongated in a vertical direction near the poles (it gets too stretched out to be useful around 70 degrees latitude). This is why you need separate polar-centred projections to view the high latitudes if you're given a Mercator map.
A Simple Cylindrical (AKA Plate Caree) projection can show the poles, but instead of being elongated vertically towards the poles the map squares are compressed.
Take a look at this link:
http://www.3dsoftware.com/Cartography/USGS/MapProjections/
The images there should illustrate the difference between the two projections. (this is actually the book I was using at work).
I
think I'm right in saying that to make a Mercator projection, you project each point on the sphere as seen from the centre of the planet onto a flat sheet that is tangential to the equator (which is why you can't see the poles in it - they wouldn't intersect the sheet). Whereas to make a Simple Cylindrical projection, you look at the sphere from outside and project each point back onto a sheet along the line of sight. (I dunno if you can visualise that easily...)
That's fair enough re: the distortions. You're never going to get it 100% right when converting between projections anyway, it's inevitable that such things will creep in. As it is your work is still very good and useful
.
As for how I projected your map onto a sphere, simple - I used
POVray. It's a free raytracer that uses a kind of programming language to design scenes. I simply made a sphere in it, used your map as a texture for it, and took a picture
. You can take a look at some of my relatively amateurish space art that I've done for it on my
Art Hub, but there are plenty of other far superior images around made using POVray. It's a very versatile program and can do pretty much everything that the expensive renderers can.