The fiction of the world has it that a spell is a formulae -of gestures, hand signs, specific words, certain materials, symbols or diagrams, whatever the formulaw says you need to incorporate- that is used to both harness and shape the innate force of magic that pervades the game world's cosmos to a specific desired effect. As we view in science, the proof of a spell's veracity is that the effect is a reproducible reliable result.
A spell is a...a "piece" of magic, a complete "packet" or a "recipe," if you like, that can be comprehended and controlled. Something that can be learned, understood, reproduced, and passed along. Something that can be -though needn't necessarily- written down. Hence, we have spell scrolls, spell books, ancient tablets of unknown or forgotten magical languages, talismans with the symbols of power etched upon them, etc...
There are some spells which can be reproduced through different means....A cleric receives the divinely powered utterance in the tongue of the gods. A mage pours over his grimoire to ensure he has the proper hand gesture to trace the activation glyph just right. A druid has been instructed over and over in properly connecting to the natural flow of magic (that forms a foundational element of existence) to glean the unknowable syllables of the sacred druidic tongue...All three produce the same spell effect, but they are not the same words (though could be in different languages) or gestures, methods or practices.
Most spells can be thought of/are more accurately described as "incantations." The right words to make the magic you want. Perhaps any magic-worker can "cast" a circle of power, with certain colored candles, the right kind of incense, chimes/bells, and repetitive chanting to produce that spell effect, too. That's a "ritual." A ritual is just a different -often lengthy- mean for casting a spell. But they are also a "spell."
Magic can be produced is a wide variety of ways. Spells are the most commonly seen/encountered. Rituals, of course, are just another form of spells. But then there are various practices, techniques, secret traditions or mastered abilities that are equally capable of producing magic/supernatural effects...but are not, themselves, "spells."
That cleric invoking the divine power (lent from their deity) to repulse the undead? It's magic! For sure. Not a spell. The druid's shapeshifting? Magic! A supernatural power produced through some secretly passed on technique/tradition/preparation (fueled by a connection to the natural magic of the world), yes. Not a spell.
The magical abilities (indeed, their very nature) of the fae or an elemental? Supernatural power or "spell-like" ability? Yes. Magic? Absolutely. A spell? No.
Psychic powers? Not a spell. Not even "Magic" as I have stipulated for the fiction of my game world. A supernatural (or occult or eldritch, if you like) power that produces a supernatural (occult/eldritch) effect. Yes. Looks like magic, because the raw force of magic is what makes things that can/should not be possible into reality, but isn't magic. What the psychic is doing is not harnessing and directing the magical forces (arcane or natural or divine) of existence. They are not -again, in the fiction- "casting a spell" to effect their powers.
Now, the separation of "spells/no spells" is not, by any means, a hard line. A vampire, dragon, fae entity, and innumerable other types of beings/creatures have supernatural/magical powers, for sure. Some may also know/study/have accumulated spells they know how to produce. But everything magical that they can do is not a "spell."
I would even submit (were I to use the class) deem that the magical effects produced by the innately magical "Sorcerer", while they can be done with words and gestures...can be done by doing the same thing over and over...still, not a "spell" - IN THE FICTION - as I've described above. But a supernatural magical power. It is probably/would be called a spell, in world, as a simple shorthand way of discussing it. But the spell-casters would know the sorcerer's power is something "else." Whether that is viewed (by normal persons or even other magic-users) with envy, awe, fear or hatred would be an entirely different conversation.
So...yeah...long story long, that's what a spell "is/is not" in my world.