By request from my mother, who I thought would never get this forum, we have:
Immolation derives from the Latin "immolare" for "to sprinkle with holy meal before offering or sacrificing" from "mol(a)" for the sacrificial barley cake (see mill and millstone derivations). It has come to mean not just the sacrifice, but the act of sacrificing, and since the sacrifice was originally by fire, immolate means to kill as a sacrifice by fire, and therefore, immolation still has the implied requirement of fire.
We don't have too many sacrificial rituals left, but there are some easy comparisons. Political statements that used to be made by self-immolation are not made by suicide bombings. The executives were too late in their immolation of the financial records before they were seized by IRS subpoena. Feeding the dying fire on a cold night is an exercise in immolating logs. Maybe, if we are praying for the fire not to go out. Since it is not killed, a phoenix does not undergo immolation as much as spontaneous combustion. The volcano immolated the forest. Again, no. The act of "killing" requires intent, and therefore, must be the act of a person (all legal pretense aside). Animals kill other animals, but not in ritual sacrifice, or I'd have some accounting to my cat when I return home. Some days, I wish I could immolate certain words from usage. Eh. Better to say expunge or eradicate. The word has a very specific usage to "sacrificing" things by fire, and limited expansion since it is quite specific. You need the connotation of sacrificing and you need a good fire. One day I hope have a "Mortgage Immolation Party". Probably not, for many reasons. When the steak slipped through the grille onto the coals it was not just charred, but immolated. Was this truly sacrificed or just an unfortunate accident? She didn't like the "special seasoning" in his burgers and "accidentally" immolated them. Ok, now it's intentional, but is is really a sacrifice or just getting of something bad.
Now, incineration derives from the Latin "cinis" for ashes, and means "to burn, to reduce to ashes". So while immolate carries the fire requirement from the process of the sacrifice, incinerate is a fire without the sacrificial overtone. To incinerate something is just to burn it, without sentiment. The crematorium normally incinerates a coffin, while other articles laid in the coffin by mourners are immolated. Preventative measures to forest fires sometimes involve incinerating scrub brush before the dry season. I have recently discovered the joys of propane in incinerating the weeds in between the paving stones of my walk. Wear gloves!