Above & Below: These two look the most similar in direct sunlight (above), but in lower lighting (below), the difference is quite obvious.
Below: In partial sun you can see how the gold glitter enhances Purple Gala, while Space Cadet shows more purple/violet glitter. I think Space Cadet's glitter is more foil-like than Purple Gala's also.
Below: A look at the colors that make up each shade reveals the dark aqua base and vivid light purple glitter in Space Cadet vs. the purple base and gold glitter in Purple Gala.
The question was asked "are they different enough that I need them all?", and even without being able to show you Dot Com, my answer would be yes. I'll refer you to photos posted by Steph's Closet and Kris Primps for a closer look at Dot Com. I will say that Dot Com and Purple Gala are more similar to each other than Space Cadet, although if memory serves me correctly, the glitter is a little more bronze--still gold, just not as bright, and the purple a touch more brown in Dot Com than in Purple Gala. Space Cadet also has some duo chrome which isn't found in the other two. If anyone else who is familiar with these 3 polishes cares to offer their thoughts, feel free to add them in the comments!
Edited: I noticed a comment about the similarities of Purple Gala to Hard Candy's Mr. Wrong, and yes they are very similar. Here's the link where I compared those two shades.