Anything that happens terminally happens at the end of something, which might be a plane ride or someone's life. Terminally describes something at the end, the last call, the big curtain coming down.
Since terminal things involve an ending or something that ends, the adverb terminally also refers to endings. Although it’s often sad, as endings are, the word itself has the courtesy to end in –ly so it’s easy to spot as an adverb. Someone terminally ill has a deadly illness. This is a word for endings: after something happens terminally, it's over.