I made the split between Divine and Nature/Natural magic many many moons ago. So there is actually a triad of magical energies, each a separate source and with a separate mode for accessing.
In my homebrew world, Divine magics are spoken/cast/known through the language of the all-but-dead empire (like how Latin used to be the language of the Catholic Church). Cleric spells are cast in Old Selurian. Clerical scrolls are written in Old Selurian. It is the cleric's (paladin's what have you) connection to the divine and the imbuing of the divine essence in them that produces the magic, "triggered" [for lack of a better term] by the proper "prayer/invocation/spell" spoken in the "sacred" Selurian tongue...not the tongue itself. It has become, at this stage of history, a language used only by the priests, some academics (to access the ancient histories written in it), and very very few ancient noble houses that still bother to learn it. One does not hear conversations in this langauge. It is for ceremony and religious rite...and divine spellcasting.
Nature magic, insofar as PC's are concerned, is cast through the archaic/secret/cryptic Druidic language. This language has no written form and so there are no scrolls of Nature magic spells. It is said that those uninitiated by the Ancient Order [of Mistwood] who hear the druidic tongue are driven mad by its primordial incomprehensible power.
Arcane magic forms the largest slice of the "magic pie chart" and is accessed via the Arkanic tongue...the hodge-podge culled together by wizards throughout the ages that are proven to produce consistent results/effects. Arkanic incorporates, to varying degrees, the ancient remnants of/words from titanic and draconic magic and tongues, some elfin language/spell construction/grammar, "cosmic" sounds and secrets such as the Words of Making & Unmaking, and a host of other syllables that, taken separately, sound like so much gibberish or mumbling...not to mention the individual flare and inflection added on an individual mage-by-mage basis. Arcane spellcasters, by necessity and definition, know and speak and can decipher [to varying extents] the Arkanic "language" enough to produce [and reproduce] the known effects they want.
"Read Magic", as the long established starting spell, does not exist. All arcane casters can read "magic" [arkanic] and thus can prepare and cast Arcane-based spells from books and scrolls...including those that might not be on their allotted spell-school lists. They can not "learn/record/memorize/prepare" those spells (not of their individual spell lists/school types), but they can read the phrases from a scroll. Those that learn Old Selurian as an additional language could, similarly, cast Divine spells from a scroll if they wanted.
Clerics, or anyone else for that matter, who can somehow learn the Arkanic tongue (simply NOT done by wizards and students of the arcane. It is held close to the vest by mages in an "initiated only" kind of way, as the Druids do with their magical tongue) could cast arcane spells from scrolls. An "Acolyte/Cleric-turned-Warlock" or "Thaumaturgist/Exorcist/Ceremonial Magician" kind of character comes to mind. Someone who has not had some formal arcane-casting training is VERY unlikely to be capable of learning it....teaching it to one's self/learning it without instruction, takes many years to get right. There are no "Universal Arkanic to Common dictionaries" floating around.
Protection Scrolls [and, in my homebrew setting, Sending Scrolls], by their nature as tools (or commodities) for the uninitiated, can be used by any class and involve more diagrams/talismans, ritual, and/or some small repeatable phrasing that has been deemed "publicly-safe" to produce its effects.
So...yeah...the Divine/Arcane split is alive and quite well as far as I can tell...the Divine/Nature split, as far as "official/default D&D fluff" is concerned needs a good deal of work.