I'm thinking the spirit is the mechanism that makes us aware of a supreme being. Our Indians had the Great Spirit in the Sky and I've read where south sea islanders had that same thing and also the indigenous people here in Australia have it too. The soul defines our character, right. The body is just a vessel like you say with that water bucket. It holds our essence, in this case the water. Has the water changed when it was poured out? Still water. If the bucket collapses and can't hold the water anymore, it's useless and thrown away, such as our bodies will be when it can no longer hold the essence of who we are.
I'm not a theologian or clergy or whatever. It's just stuff I've picked up along the way...
Since animals don’t seem to have a sense of good or bad (spiritually), there is a circle there which would assert that animals don’t have a spirit, though they have a soul of life, and this same circle would close back on the notion that without a spirit animlas have no sense of God their creator or of things regarding His nature. But I tend to believe animals can project love, and that’s one of God’s aspects, so who knows?