Both patterns are typically worked on even numbers of stitches (though Seed Stitch can also be worked on an odd number of stitches, with a slight variation in the pattern) and both involve rows of knit 1, purl 1 across alternated with rows of purl 1, knit 1.
The difference? Seed Stitch involves one row of knit 1, purl 1 followed by one row of purl 1, knit 1, while Moss Stitch uses two rows of knit 1, purl 1 before two rows of purl 1, knit 1.
So Seed Stitch ends up with single knits stacked on top of single purls and vice versa, while Moss Stitch looks like two rows of ribbing that are then shifted one stitch.
I wish I had a clever mnemonic to help you remember which is which, but I have to admit that even now I sometimes confuse the names in my mind! It's just something you have to try to memorize. Either way, though, you're adding lots of simple texture to your knitting patterns.
Either stitch is great for allover knitting, to use as a border or hem, or anywhere else you might want to use it!