I'd like to take some levels as a Wizard; in-game, the Wizard in my party teaches me some magic so that I can become a practicing Wizard. But, I haven't come up with a reason why I don't have exactly the same spells as my teacher.
In fact, I am not 100% sure how I get new spells as a Wizard. When I gain a level as Wizard I can add two new spells to my spellbook. For me, this brings up a lot of questions.
Do I have to find these spells first, for example on a scroll or in another spellbook? Would I need to pay 50 gp and spend 2 hours learning spells, per spell level? To me, that doesn't make any sense. So, I assume that I just pick two new spells with each level and additionally I can add the spells I find to the spellbook.
Do I “invent” the spells, e.g. “I would really like to be invisible, so I'll figure out a spell that makes me invisible”? I think that'd be an odd way to go about it. Perhaps it goes more like, “Oh, I remember that one afternoon when my mentor tried to explain how Fireballs work; now I finally understand it, so I can cast Fireball from now on.”
Summary Question: Where do the two new spells come from?
Best Answer
Your spells come from research, experimentation, and epiphanies as to the Weave of magic.
The boxed text on PHB pg 114 has a bit of flavor as to why this is so:
PHB pg 112 gives you more context to use for your flavoring of your dive into the Arcane arts of a Wizard multiclass:
Did you find a mentor to teach you your first few spells? Do you carry around a very old Tome of spells you have slowly started mastering page by page? Did you decide "Hm..I'd really like to call down a Meteor Swarm one day." And when you finally figure out the magic involved you trademark it and start teaching all the younger wizards 'Airatome's Volatile Meteor Swarm' because the spell now exists because you created it?
That's all up to you.
(To directly comment on your In game reason.... keep in mind the moment you get a spellbook as a Wizard you can, actually, copy the spells your original party wizard knows from his own spellbook if he and the DM allow it. Doesn't mean you have to use them...just means on top of your level 1 spell allotment, you can also copy what he/she knows when you are of sufficient level to do so. Your in game reasoning for using different spell loadouts is because while your party wizard started you down the path to magic, you found your own 'School' to conduct your own studies in to.)