But the actual mechanics of divine magic and arcane magic are the same. The spells are written in the exact same format, both have saving throws to avoid their effects, both are limited to a small number of castings per day. In most editions both were fire and forget. Clerics getting healing and Magic Users getting fireball was a difference in spell Iists, not anything intrinsic to the mechanics of how spells actually worked. If you were to write up a totally original spell, never seen before in standard format it would not be possible to tell from reading it if it was a divine or arcane spell. In 5e all the spells are listed together in alphabetical order. Without the spell lists there is no way to know which spells go with which class or which are divine or arcane.Also that healing magic is divine only. Arcane casters are never allowed to have actual healing spells.
To say that healing magic is divine only, not arcane is a distinction you can only draw by looking at the spell lists. You can't tell from reading the rules for the spells.
This is what I mean when I question whether the distinction is even real in D&D. Spells all work exactly the same way. It is purely cosmetics whether they are divine or arcane. There is not even a written rule stating that all healing magic must be divine because arcane magic can't do that effect. there is no reason an AD&D Magic User couldn't create a new healing spell with the mechanics of the Clerical Cure Light Wounds spell, except Dungeon Master fiat saying "No, you can't do that." Nothing in the rules would prohibit it.