There are many differentt types of casters in dungeons and dragons. You have full spellcasters, such as wizards, warlocks, sorcerers, druids, clerics, and bards.
The half casters are paladins, rangers, and artificers.
Then there are the third casters, which so far are only subclasses like eldritch knight fighters and arcane trickster rogues.
These spellcasters are labeled full casters because they all get spell slots up to 9th level, and all gain cantrips as they level up.
Bards are the most unique full casters. While most get their powers thanks to their studies, a devotion to a god or nature, or being born with them. However, a bard's power is their voice. Whether they use song, poetry, or simply wit, they can muster up magic.
Clerics and Warlocks go hand in hand, both being devoted to gods, but in different ways. A Cleric is a disciple of a god, praising and worshipping them while being granted power for doing so.
Druids have a natural form of magic, drawing their power from the nature around them. This allows them to summon animals, or even turn into them. Though, wildlife is not their limitation. They control almost any form of nature, including water and vegetation
Sorcerers are looked down on by most other full casters, as they are born with their abilities rather than putting in the work seen by most others. Their magic is in their bloodline, whether they're descendants of a dragon, or maybe even a tiny fairy.
Warlocks are a more transactional type of caster compared to Clerics. While a Cleric may act based off of the ideals they learned from their god, Warlocks are bound by a contract with a patron, normally a god. And so they have to fulfill their patron's wishes if they want to keep their power.
Wizards are the most common full casters, as most who possess magic obtained it through years of study in the ways of mystica, keeping an object to help them channel their spells through.
Half casters are an interesting bunch, as their spells slots only reach the 5th level, and they gain their spells at half the rate of full casters. Oddly enough, only one half caster class gets cantrips, and those are artificers.
Artificers rival Wizards in intellect, as they use their magic to bring advanced mechanizations to life or simply make a mystical item that they came up with in a dream. Either way, they're more involved in autonomy than spellbooks.
Paladins, though believed to be very righteous, do not get their powers from some divine being. Instead, they devote themselves to an oath that they swore to always follow. Though, not all paladins follow an oath, so be cautious if you think you may be talking to an Oathbreaker, because they're bound to no code at that point.
Rangers, unlike Druids, do not fully devote themselves to all of nature, so they have less power than Druids, but still draw on nature to cast their own spells.
Simply put, third casters are an even more diluted form of half casters, as they don't learn cantrips, their spell slots only go to the 3rd level, and gain spell slots at a third of the full casters' rate.
Eldritch Knight Fighters are great at subverting expectations, as while you normally see spellcasters in the backlines, these guys have studied combat in a physical and magical way, allowing them to hit you with a club before sending a blast of fire at you.
Arcane Trickster Rogues are powerful, because while you may think they are just very stealthy, they can teleport through the shadows using techniques you've never heard of, making them much more silent but deadly.