I think Christian theology (sometimes) distinguishes between soul and spirit in that it is the spirit that allows humans to commune with the divine Holy Spirit. Nevertheless, there is no clear consensus and the numerous passages connected to this idea, both in the Old and New Testaments, are open to interpretation, especially owing to the fact that they have been translated so many times – with all that entails. Nevertheless, leaving aside the semantics, there is plenty of scripture to support the notion that animals are not mere biological automatons, here only for our exploitation, in fact, there’s plenty of scripture that affirms the complete opposite. As I indicated before, why would Saint Francis of Assisi have preached to the birds? Why would the Bible include verses about all of creation singing the glory of God and so on? Christian theology might also point to the story of Noah and the flood, the animals were saved too.
So, in Christianity, when it comes to whether animals have souls, spirits, spirits and souls etc., there is no single defining verse in the Bible that unequivocally states they do nothave some form or other and plenty to the contrary. I would argue that Christianity teaches that all life is precious to God, God’s breath was also breathed into living creation – the idea of breath being soul or spirit.
As for the often-quoted passage in Genesis about “dominion”, well, the Bible does indeed state that, but what is dominion? It means stewardship, it means looking after and taking care of the world, just like a person would look after, care for and protect anything else under their stewardship; therefore, if we look at what is happening in the world today in environmental terms – wholesale destruction of natural habitats, pollution, unsustainable exploitation of resources and so on, I don’t think that we can justify any of it by pointing to “dominion”.