Didn't God give Adam "dominion" over all other forms of life? And wouldn't that mean, and I hesitate to make this look like a logical conclusion on my own, that the soul or spirit of animals is different from that of humans?

Genesis 1:26

26 And God said, Let us make man in our image, after our likeness: and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepeth upon the earth.
KJV

Genesis 1:24-31

The image of God consists, therefore, in the spiritual personality of man, though not merely in unity of self-consciousness and self-determination, or in the fact that man was created a consciously free Ego; for personality is merely the basis and form of the divine likeness, not its real essence. This consists rather in the fact, that the man endowed with free self-conscious personality possesses, in his spiritual as well as corporeal nature, a creaturely copy of the holiness and blessedness of the divine life. This concrete essence of the divine likeness was shattered by sin; and it is only through Christ, the brightness of the glory of God and the expression of His essence (Hebrews 1:3), that our nature is transformed into the image of God again (Colossians 3:10; Ephesians 4:24).
(from Keil & Delitzsch Commentary on the Old Testament: New Updated Edition, Electronic Database. Copyright (c) 1996 by Hendrickson Publishers, Inc.)

Genesis 1:26-29
In our image, after our likeness. This was a peculiar distinction, the value attached to which appears in the repetition of the idea by a different but synonymous expression. And in what did this "image of God" consist? Not in the erect form or features of man; not in his intellect, because the Devil and his angels are in this respect far superior; not in his immortality, because he does not have, like God, a past as well as a future eternity of being; but in the moral dispositions of his soul, commonly called original righteousness (Ecclesiastes 7:29). Since the new creation is only a restoration of this image, the history of the one throws light on the other; and we are informed that it is renewed after the image of God, in knowledge, righteousness, and true holiness (Ephesians 4:24; Colossians 3:10).
(from Jamieson, Fausset, and Brown Commentary, Electronic Database. Copyright (c) 1997 by Biblesoft)

OT:1961
hayah --



to be, to become, to come to pass, to exist, to happen, to fall out

a) (Qal)
1) to befall
a) to happen, to fall out, to occur, to take place, to come about, to come to pass
b) to come about, to come to pass
2) to come into being, to become
a) to arise, to appear, to come
b) to become
1) to become
2) to become like
3) to be instituted, to be established
3) to be
a) to exist, to be in existence
b) to abide, to remain, to continue (with word of place or time)
c) to stand, to lie, to be in, to be at, to be situated (with word of locality)
d) to accompany, to be with
b) (Niphal)
1) to occur, to come to pass, to be done, to be brought about
2) to be done, to be finished, to be gone
(from The Online Bible Thayer's Greek Lexicon and Brown Driver & Briggs Hebrew Lexicon, Copyright (c)1993, Woodside Bible Fellowship, Ontario, Canada. Licensed from the Institute for Creation Research.)