Thinking about the tomato analogy for stats, I came up with an interesting analogy to explain how different classes learn to harness magic. My group of new players all found it very comprehensive and useful, so I thought I'd share. Not covering every single way various martial classes can learn spells, but I think the analogy is flexible enough.

Basics

First, imagine that every caster has a rubik's octahedron (8 sides for the 8 schools of magic)

Different patterns result in different spells. A solved rubik's octahedron is equivalent to the wish spell, while randomly shuffling it results in wild magic.

Cantrips are a single face on a single piece. Once you have a firm understanding of that piece, it's easy to find, and always accessible.

Preparing spells is equivalent to getting the octahedron in a certain state where your prepared spells are only a few twists and turns away. You haven't forgotten your other spells, they just take more time to get to.

Now onto the casters:

Wizards

Wizards are the hardcore PhD students. They learn the specific moves and patterns, as well as the exact breakdown of a pattern, and how the orientation results in different spells. Hence why they need a spellbook. Certain wizards focus on figuring out all the properties of a single face, thus mastering a specific school of magic.

Sorcerers

Sorcerer bloodlines are like instincts. Past memories let them perform moves by pure reflex to reach patterns, yet they lack that in depth knowledge.

Bards

Bards have their colleges where they learn how to translate twists and turns into notes and tunes in order to create elegant patterns.

Clerics

Clerics are given the paths to these patterns through guidance from their deity.

Druids

Druids discover these paths and patterns from communing with nature itself. (Find the contra cheat code in the stars)

Warlock

Warlock patrons just rip off a chunk of the octahedron, and slap on a replacement that says "Eldrich Blast".

Artificer

Artificers learn the patterns themselves, but rather than the paths/moves to reach these patterns, they just remove the stickers and put them back in the order they want.

Paladin

Paladins learn a little from their cleric buddies, but lose focus when they learn any combination lets them use divine smite.

Rangers

Rangers learn a little from their druid buddies, but it's just an additional tool, not a primary focus.

Arcane Trickster Rogues

Arcane trickster rogues stole the wizards notes, but can only make out bits and pieces of their messy handwriting