Hi Catherine.
With regard to the possible immortality of humans and whether the bible indicates any difference between humans and animals in this regard, I must add further to the post above.
The Hebrew language has five different words that get translated as “soul”: **nephesh, ruach, neshamah, chayah and yechidah.
**
Nefesh is the physical life force of the body. Of course, all animals have this.
But Chayah (Which literally means “living.”) is used in Genesis 2:7 , where God breathed the breath of life into Adam and then Adam “became a living soul (nephesh chayah).” Note that this term combines nephesh, the life force of the body, with chayah, “living.” But isn’t a body with nephesh already living? But ‘chayah’ means to sustain life or to live forever. So, the question I leave you with is what ‘nephesh chayah’ means which applies to humans and humans alone.
God bless