A wizard to me is someone who has studied magic and knows his lore he uses his brain not innate ability to wrestle with magic. Some examples are the wizard from Dragonslayer , Harry Dresden he reminds me of a lot of DnD wizards with his comments wizards are powerful when they have time to prepare and as we know Harry often does not have time. Raistlin is another wizard who fits the bill for me.
Merlin was never a wizard in my mind more a druid. That is how I picture him when I read the tons of Arthurian books I own.
I guess for me the term wizard, sorcerer, witch, mage are often interchangeable.
I quoted your post because it matches a lot of what I was going to say.
Dragonslayer is one of my favorite movies, so it's a big influence on how I view rpg adventures in general. I've only recently become familiar with Dresden, but he has a lot of traits which I associate with 'wizard.' Likewise, I view Raistlin as a wizard; the Dragonlance books are what introduced me to D&D.
I had never thought of Merlin as a druid, but I suppose that does make some amount of sense. Still, I do tend to view him as a wizard, but I also feel that he's above and beyond what lesser casters can do, but his downfall is that he's attached to a version of the world which is slowly being replaced.
Oddly, even though she was a big part of the stories I'm familiar with, Morgan le Fay is not someone I typically think about when thinking about my view of what a wizard is. For some reason, my mind just doesn't make that connection. One of her defining characteristics was being able to use magic, but I don't often think of her.
As a few others have said, I don't really view Gandalf as being a wizard either. To some extent I do in so much that he certainly fits some of the wizard stereotypes, but he's also pretty obviously more than just a simple man who knows magic. All things considered, I suppose maybe I do view Gandalf as a wizard, but I also recognize that there's something more to him than that.
In contrast to what I just said about Gandalf, I do view Jadis (The White Witch from The Chronicles of Narnia) when I think about spellcasters. I say "in contrast" because it is heavily implied that she's not fully human, but -for whatever reason- I easily view her as a caster. I'm not so sure I view her as a wizard, but the character of Jadis is a pretty big influence on me. I'm positive that I don't view her as a D&D wizard because her ability to fight in melee is far better than the D&D class would allow, but I do view her as a mage when it comes to rpgs in general. She's a big enough influence on me that I've pretty blatantly used her as the basis for a villain I had in a campaign I ran. I view her as embodying multiple archetypes - BBEG, persuasive villain, magic user, and a few others.
I'm a big fan of R. Howard's writing, so most of the Conan and Kull stories are an influence on me. Likewise, while they differ quite a bit from the original stories, the movies starring Arnold Schwarzenegger are an influence; in particular, Akiro the Wizard is someone I view as an archetypal wizard . The scene where Akiro and the enemy wizard are dueling over trying to keep a gate open/closed is a big part of how I view wizards. (While I did also enjoy the newer movie with Jason Mamoa, there really wasn't a lot in the vein of spellcasting which stuck out to me, but I will say the movie gave me a lot of ideas for encounters.)
While I wouldn't say I view him as a wizard per se, Morgan -the main character from The Riddle Master Trilogy- has some influence on how I view magic and going on adventures in general, and the part of the book where he learns he can control fire is something that sticks with me. Likewise, as a child I read
The Chronicles of Prydain, and that book series has an influence as well. I suppose I read a lot of fantasy books that were influences on me, but it's been so long that I don't remember what a lot of them were.
The Last Unicorn comes to mind, but I don't think that is something I remember as an influence on how I view wizards; it's just something I remember reading.
Somewhere among all of the things I experienced during my younger years, I'd also say the older Final Fantasy games had some amount of influence on me as far as the idea that magic could be divided into colors and that mages often wore funny hats. In general, I would say some of the old NES rpgs were among the biggest influences on me when it comes to how I view rpgs, and I'd go so far to say that I may not have ever played tabletop games had I not become interested in games such as Dragon Warrior, The Bard's Tale, and various others. To varying extents, those games had some influence on how I originally viewed what many elements of an adventure should look like. My views have evolved a lot since then, but those were part of my roots. I credit NES rpgs, choose your own adventure books, and Dragonlance with leading me to tabletop gaming.