@Eeveeinheat  

 
This is the distinction between Sorcerers and Wizards in pen and paper games like D&D and Pathfinder.
 
Wizards are taught. They use a spellbook where they inscribe their spells. They must learn the exact steps to cast any particular spell, including spoken and physical components (hand-gestures.)
 
Sorcerers, on the other hand, are born with magic ability instilled in them for a variety of reasons. They don’t need to learn magic. It comes naturally to them. They don’t need to use a spellbook, but for most spells they still have to perform the vocal and/or physical steps. Plus material components if the spell has any, same as for Wizards.
 
Why choose Wizard over Sorcerer then? There are trade-offs. Wizards can learn a far wider range of spells, but they can only pick so many at a time. Let’s say out of a possible (made up number) 30 spells, they can only choose 15 and cannot change any of them out until the next day. They also cannot cast a spell more than once per preparation. So if you want a Feather Fall spell multiple times, each copy takes up a spell slot. You also have to prepare your spell list every in-game day. If you don’t prepare it (like if you forget), you can’t cast it (preparing = choosing.) Use up your allocated spells for the day, and you’re down to using physical weapons until the next day.
 
Sorcerers, on the other hand, don’t need to prepare spells. They have their entire repertoire of spells available at one time, but they have a far-more limited selection of spells in total. Since they don’t prepare spells, they don’t need to have multiple copies of the spell ready. All of their spells share a “casting pool”, which dictate the limits for the day. So a medium-level Sorcerer might get a pool of 9/6/5/3/2. Which means 9 casts of a level X spell, 6 of a level Y, 5 of a level Z, and so on. The lowest level spells, level 0, are unlimited. The higher you go, the fewer casts you get. As you level these limits increase.
 
Just throwing some classic magic rules into the discussion.

@The Smiling Pony  
she was learning magic from magic books shortly before she teleported the table  
I’ve always liked the fanon that Trixie actually had the chops to make it into PCSFGU a few years before Twilight and Moondancer’s class but had to drop out for [DRAMA] reasons, and all of her low-end-but-highly-functional magic was essentially self taught so she could make a living with it.

@Eeveeinheat  
I’d imagine that relates more to power or “wild magic” than concrete spells.

@The Smiling Pony  
Starlight pretty much admitted to her emotions controlling her magic. So while so ponies need books, some can just will it.

@TexasUberAlles  
It was fairly clearly explicitly shown that she was learning magic from magic books shortly before she teleported the table; ie. the transmutation spell was almost certainly a spell she’d learned shortly before the episode start off a book, not just Jedi “will it” stuff.

@The Smiling Pony  
If yelling at inanimate objects was enough to give you magic superpowers, I’d be like freakin’ Tirek after he ganked Discord’s Chaos.

@onepone  
Well, she saved the nation, got recognition for it, and yelling at table salt lead to her improving in magic to level similar to S1 Twilight.

In season 1, clearly Trixie was a brilliant stage performer. In season 7, she spends her day yelling at table salt. What a life she’s lead.

@KingKek42  
To be fair, logical ideas of difficulty don’t seem to matter in this show. After all, crossing an orange with a bird is somehow easier than changing a pony’s gender according to the show.

Who would’ve thought that turning something into something else entirely would be more difficult than making a cloud?

@Starswirl  
I wouldn’t call it ‘some’.  
I came to the fandom in EG 1 and I still caught the waves, roars and walls of text.

@Starswirl  
Again, none said Trixie had ever been super powerful, or more powerful than Twilight, or as powerful as Twilight.  
There is a wide range of possibilities between “as powerful as the element of magic” and “only capable of illusions”. There is nothing in Boast Busters that imply, or suggest, that Trixie is not capable to do real magic. Surely not the fact that she had been uncapable to defeat the Ursa, since not even Twilight tried to defeat her power-wise.

@Archonix  
Best pony!

@rdibp  
she’s gweat and powerfuw!

@Archonix  
“Twixie” c:

Everyone is forgetting: Twixie is a stage magician. Slight of hand - or the magical equivalent - would be her primary stock in trade. She doesn’t need to teleport or transmute objects for all of these tricks, she just needs to slip them into place unnoticed. It takes a great deal of skill to do that.

@Background Pony #99D4  
Those things are not mutually exclusive. Not only did Twilight know more, she also showed she was indeed infinitely more powerful than Trixie was. Lifting the Ursa Minor right before it could crush Trixie proved that. Twilight was terrified during the episode because she’s so powerful and feared her friends would shun her for it.

@ArrJaySketch  
None said Trixie had ever been super powerful.  
The bolt had the same effect than Alicorn Twilight’s blasts had on the bugbear in ep. 100, and is no wonder it didn’t leave a permanent mark on something that seems to be made out of stars and thin air.  
The joke was not that the poor Trixie wasn’t powerful at all, while Twilight was super powerful. Twilight not even tried to confront the Ursa power-wise, cause the opponent was too powerful for anyone. The joke was that the boastful Trixie didn’t know what she was talking of, while Twilight did. Enough to know that they were facing an Ursa minor, that could be soothed.

@The Smiling Pony  
Agreed! I was only thinking of her initial appearance. c:

@The Smiling Pony  
Aye. Especially since many a pony questioned Starlight’s incredible magical power compared to Twilight, who had several seasons showing her working on her spellcraft… the decision to have Trixie suddenly become so powerful with what appears to be next to no effort is a strange one.

@ArrJaySketch  
(At least not until now… transmutation and teleportation in one day seems like a big deal)

@Background Pony #99D4  
Instead of summoning a vast, intense storm, the joke was that she summoned a single dinky cloud, and one that caused more surprise than actual pain. The burn mark disappeared in the next scene. You might even say it appeared to be an illusion.
 
Instead of binding the Ursa’s legs together, the joke was that she only managed to bind two fingers.
 
The whole joke was that she wasn’t powerful at all. Those were gags.
 
Trixie has never been super powerful.

@rdibp  
But Twilight is an expert in magic and a prodigy. A spell that’s tough for her to learn, will be hardly easy for someone else.

@Badumsquish  
To me, it would have had no sense for Trixie to know the spell (and to use it instinctively, as the first resource), if she had not the necessary strenght to make it effective. Moreover, the “taser spell” is much rarer than the standard blaster spell. We have seen only Luna-Nightmare Moon using a similar one.  
My headcanon is that, since the Alicorn Amulet gave to Trixie enough power to incinerate RD, and she only wanted to make her suffer, she was holding back when she threw the first one. Then she tried again with more strenght, but RD dodged.

@Background Pony #99D4  
The spells Trixie were performing in Boast Busters, like the flower conjuring and the rope levitation, were all spells meant for her act. Spells that she was probably performing for years. A lot of Trixie’s spells in the past seemed to serve no practical use as apposed to transmutation, which is obviously higher level magic.
 
Twilight’s line about the transmutation spell in Too Many Pinkie Pies being a toughie only applied to her since it was a spell she was just starting on.