I think that the death process was both spiritual(immediate separation from God during the expulsion from the garden, which we see in Gen), coupled with the physical death process.(over time)
If Adam and Eve would have died physically that day, then we wouldnt be having this conversation.
Therefore, it is speaking of a spiritual death, regarding the day they sinned.(obviously)
Look at this....
Ezekiel 18:20
20
The soul that sinneth, it shall die. The son shall not bear the iniquity of the father, neither shall the father bear the iniquity of the son: the righteousness of the righteous shall be upon him, and the wickedness of the wicked shall be upon him.
A soul can actually die....our soul is part of us.....our soul desires to sin and our body acts on that sin....God desroys both soul and body into hell....
Matthew 10:28
28 And fear not them which kill the body, but are not able to kill the soul: but rather fear him which is able to destroy
both soul and body in hell.
The body and soul are connected together on earth for all the living.
When
we sin, the soul is separated from fellowship with God in spiritual death and the body eventually follows suit.