Okay so to answer the OP's question:
Most of the videos etc. you are probably finding on YouTube are probably pre-patch 1.19. So yes, it would be confusing. I am sure SE will release a bunch of promo stuff over the summer to gear up to 2.0.
Conjurer: Many will tell you 'Conjurer is a healer'. This is somewhat true, as CNJ does in fact learn all the CURE,RAISE,PROTECT,STONESKIN spells. However, because classes are meant to be soloable/for small parties, CNJ also is the class that natively learns AERO and STONE type spells. Therefore CNJ is a hybrid between healer/nuker. If it helps to know a little background, Conjurers are from Gridania, a town that communes with the elementals and forest surrounding it. (Think something akin to a Druid Priest). Aero and Stone type elemental spells were most likely assigned to CNJ rather than THM because they are both healing/protecting and damaging in nature. Air is needed for breath but can also destroy as a Tornado, Plants need soil to grow, but an earthquake can topple a tree.
Now it is also important to know that CNJ is the primary class needed to unlock the job, White Mage. White Mage is actually the ONLY true healer in the game at the moment. In addition to all the spells it gets from it's native CNJ, White Mage also learns Regen, Holy, Esuna, Benediction.
Thaumaturge: Many will tell you 'Thaumaturge is the nuker' This is true. But it's not the only class capable of nuking, nor is it always the 'best'. Thm is the 'less-developed' mage class atm in my opinion because it basically plays like the job Black Mage, but without any of the cool abilities or Convert. So you have MP issues at times with this class. That being said, THM can do some major damage, and occasionally it is good strategy to have someone come to a battle as a THM over Black Mage because they have some AOE buffing potential/can back up heal (by equipping CNJ abilities) that a BLM doesn't have access to.
Thaumaturge learns: THUNDER, FIRE, BLIZZARD-type spells. Also, by casting these spells, you can enfeeble a mob. Blizzard can add gravity for example. You also learn SLEEP. In addition to your spells, you gain access to abilities that either increase the potential damage output of your next spell, heal a portion of your HP's based on the damage of your next spell or can be used with a CNJ ability to AOE buff the party (the buff grants HP/MP in relation to damage taken over a short period of time).
Thaumaturge also is the primary class that unlocks Black Mage. Black Mage can use all of THM's native spells but also gains the 'Ancient Magic' version of them, FLARE,FREEZE,BURST...also you get CONVERT. Convert swaps your HP's for your MP and can be used (depending on gear setup) around every 5:30 mins.
Lastly, not to confuse you more but when playing the class Conjurer, you can equip some but not all of THM's spells and abilities. So it IS possible to see a CNJ cast Thunder in a video made post 1.19. It is also possible to see a Thaumature cast Cure post 1.19. But in order to do this, the player had to equip a non-native spell from the other class. You will not see a BLM cure or a WHM cast Thunder however, as these Jobs cannot equip those spells.
I hope this helps you a little.