God said Adam and Eve would die on the day they ate from the Tree of the Knowledge of Good and Evil (Gen. 2:17), but they didn’t die that day. Does this mean the “death” God referred to was different to literal death (e.g., bodily decay or a separation from God)?
Fact 1: God told Adam that on the day he ate of the fruit of the knowledge of good and evil he would surely die:
Genesis 2:16-17 And the LORD God commanded the man, saying, “You may surely eat of every tree of the garden, (17) but of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall surely die.”
Fact 2: Adam did not actually die on the day that he ate of that fruit.
Various attempts have been made to explain this difference, including the two that you mention. Maybe it was a spiritual death by the separation from God that started that day. Maybe it was a process of mortality that was started that day. Neither answer meets the conditions of the threat. God did not threaten: “You will be separated”, nor: “You will become mortal”. He actually said: “On the day you eat of it you will surely die”. A far simpler explanation is that God forgave Adam due to his repentance. This does not mean that Adam got off without consequences. There are other cases where someone was forgiven of a crime for which the punishment is death, but still suffered serious consequences. There was no other legal punishment that was appropriate for the crimes of David of adultery and murder. However David’s humble repentance meant that God was willing to forgive David, but with consequences:
2 Samuel 12:10-12 Now therefore the sword shall never depart from your house, because you have despised me and have taken the wife of Uriah the Hittite to be your wife.’ (11) Thus says the LORD, ‘Behold, I will raise up evil against you out of your own house. And I will take your wives before your eyes and give them to your neighbor, and he shall lie with your wives in the sight of this sun. (12) For you did it secretly, but I will do this thing before all Israel and before the sun.'”
All these calamities befell David, despite his repentance and God’s forgiveness.
Similarly we may repent of some serious crime, and be forgiven by God. That does not mean that we do not face the legal consequences if the sin we committed was also illegal, or perhaps the medical consequences if the sin we committed affected our health.
Adam’s repentance is hinted at by the covering of animal skins to hide his nakedness, and by the ritual of worship that was instituted in his family, as seen in Genesis 4. If Adam had not repented he would have been killed on that day as threatened.
Adam’s actual punishment is described:
Genesis 3:17-19 And to Adam he said, “Because you have listened to the voice of your wife and have eaten of the tree of which I commanded you, ‘You shall not eat of it,’ cursed is the ground because of you; in pain you shall eat of it all the days of your life; (18) thorns and thistles it shall bring forth for you; and you shall eat the plants of the field. (19) By the sweat of your face you shall eat bread, till you return to the ground, for out of it you were taken; for you are dust, and to dust you shall return.”
But the threatened execution on that very day was not required.