Ya, paint bucket and selection are 2 different, independently working tools.
Selections can be anti aliased as well as bucket fills (that usually happen automatically).
Make sure to switch anti alias off for everything you use.
You'd probably be better off with the blend tool than with the bucket tool anyway since you don't really need a bucket fill if you have something selected, you just want to slap a solid color over it and the magic wand is a more than capable replacement for that paint bucket.