Outside of D&D, whenever anyone thinks of a gnome, they are more likely to think of a "garden gnome" or (something along the lines of "David the Gnome"), not how they are presented in D&D.
There's plenty of information out there about gnomes in-universe, but out of universe, why are they as they are and not more like garden gnomes (i.e. Tiny Fey creatures, most likely)? What influences inspired the D&D gnome as it first appeared, and continues to appear today?
This came up because I was recently getting a couple of people into D&D using the 5e starters set, but I also brought the PHB along to allow for all races and classes (since I wanted them to have more variety whilst creating characters). I was describing each to them, and all the other races made sense to them, but then we got to gnomes.
What they imagined were garden gnomes, whereas what I was describing sounded more like an alternative to a halfling. The best way I could describe it in the end is basically like a more magically-inclined halfling; "they are to halflings what elves are to humans", which they accepted (in a "if you say so..." kind of way) but it still brought to my attention how weird it is that gnomes are what they are in D&D.
So, how come gnomes in D&D are as they are and not more like garden gnomes or another more common depiction of gnomes?
Note: I am not asking about wanting to change them in any way, since I like D&D gnomes as they are, but it doesn't make much sense to me as to why they are like that to begin with. This also isn't about why they're not considered Tiny in 5e since all playable races are Small or Medium in 5e.
I am definitely not asking for designer-reasons that can only be answered with Crawford tweets or whatever, nor anything from Gary Gygax back in the day (although these sorts of quote won't be rejected either; they're just not mandatory), simply what other depictions of gnomes exist that differ from the garden gnome that may have influenced how they currently are in D&D.
This isn't about any system in particular, hence why this isn't tagged dnd-5e but rather dungeons-and-dragons, since as far as I can tell, they've always kinda been as they are presented in 5e throughout all editions, although I only really know about 3.5e (via NWN2) and 5e.