Okay, "Other" is not an issue. There will always be some Other on an iPod. You only need to do something about it if it becomes too large. (644MB is not.)
But now that you have confirmed one or two things, let's analyse your library
If all your songs all had a Bit Rate of 256Kbps, 6.3GB would be approximately 778 songs. By contrast, in my Library, if I look at songs with a Bit Rate of anywhere between 279Kbps and 320Kbps, then just 393 songs take up 6.3GB. Notice the difference.
As the songs you purchased from the iTunes Store will have a Bit Rate of 256Kbps, it suggests that the "few ripped albums" that you mentioned are at a higher Bit Rate than this. So let's check them.
In your Library, highlight a few of the songs that you've ripped (from CD, or vinyl?). In Windows, right-click and choose Get Info/Summary>Bit Rate (sorry, don't know the Mac command). What Bit Rate are these ripped songs using?
I know it's all asking questions at the moment, but with a couple of tips (to follow) you will be able to reduce the space taken up by these songs.
One thing though; I don't undertsand how the same 633 songs can only be using 1.6Gb on your iPad. Not only is the difference odd, that figure is not a lot, despite what you may currently believe. In fact, it's far too low! If I look at 48 songs in my Library at 128Kbps, and the rest of my songs at lower Bit rates, I could get a total of 139 songs in 1.6GB. But some of your songs must be at 256Kbps, and I wouldn't want to listen to music at a Bit Rate of 32Kbps, which is what would be needed.