Decades ago my then 1+ -year old daughter had a cold. At bedtime she was wiping her nose on a soiled tissue. “Don’t use that, it’s dirty,” I said. “Wait, let me get you a new Kleenex.” The next evening she asked for an “X.” A clean X instead of a dirty one.
Not sure if it fits the grain of this thread, but…
I really felt silly when my daughter taught me how to eat string cheese. As an adult, never having had this in my youth (not sure if it was sold prepackaged in the 70s), I just opened a pack and started chomping down on a stick of cheese.
She looked at me aghast and demonstrated how one peels apart the cheese, like stripping wood fibers off of a tiny log. That’s when I understood why they call it string cheese.
That is just about the most adorable thing I’ve heard this year! 
My 10 month old son is used to hearing “want noomies?” if it looks like it’s time to nurse. For the past month or so, though, if I give him a regular snack (a vanilla wafer or some such) he’ll sing to himself “noomanoomanoomiee!!”
I think my 13 y.o. son is gaslighting me about the times of his wrestling practices/meets (to get out of chores? who knows?) or I’m getting early onset Alzheimer’s, but it’s entirely too stupid to explain.
We still refer to mud puddles as muddles, because that’s what my daughter called them. It makes perfect sense really.
My young son once announced he knew how tissues were made: “They use hemorrhoidal!”
After reading “The Three Little Pigs”, my four year old daughter asked, “Do, we live in a brick house”?
I replied, “Of course”!
It was bedtime. I couldn’t tell her we lived in a stinkin’ trailer.
Must be that lateral thinking I’ve heard about.
A family friend who recently had a baby. We told our four-year-old son that the friend would be visiting us, and he protested, “She’s not a friend, she’s a mommy!”
Interesting how his concept of taxonomy forbids placing a person in multiple categories!
That’s beautiful. Is it too soon to show her the real numbers and imaginary numbers displayed as a simple graph with x-y axes?
You’d have to explain negative integers first, and maybe then just say that there’s this number which is so weird, it generates a whole 'nuther “side-to-side” set (no need to get into square roots per se, just yet).
I’m only half-kidding about this – she may find the ideas cool, even if it’s way, way too soon to grasp most of it!
My son is just about four. Somehow the term “shellfish” came up one day.
Son: What’s a shellfish?
Me: It’s an animal that lives in water, and it’s covered by a shell. Like a lobster or a crab.
Son: And a turtle!
Me: No, they’re not shellfish.
Son: They have a shell.
Me: But they don’t live in water.
Son: Sea turtles do!
Me: Uh… I guess they do, at that. Well, time for bed!
I had to look up the definition to re-learn that shellfish are invertebrates.
That tool that the doctor uses to test your reflexes is, coincidentally, known as the quarter pounder.
I is fibber.
My daughter 18 mos/2 YO and at the time was naming animals by the sounds they make. We were watching Fantasia and the *Rites of Spring *section came on, showing the little Pegasus ponies flying up to sleep in nests in the trees.
She gaped with awe and then softly said “neigh-birds”. I’ve always loved that.
My parents took us to the movies starting when we were pretty little (I attended 2001 in utero :)) and I apparently had some interesting ideas of how that worked. I thought there were a bunch of people standing behind the screen speaking the dialogue. Then at one particular movie Barry Lyndon I wondered how much the actor had to be paid to let them amputate his leg for the role.
Time to start teaching complex numbers!
It was pretty typical college kid food in the late 70s. Or at least it was for this then-college kid.
I suspect the OPs story is related to the issue of Theory of Mind (although not quite the same thing). Children of a young age can’t tell that other people have their own minds, and might not necessarily know the same things as the child does. At some point every child (barring autism disorder) gets that other people don’t necessarily see things as they do, but before that occurs, interesting consequences follow. The Sally-Anne test is designed to pick this up.
You show a kid a box that looks like a box for chalk. While another child (“Sally-Anne”) is out of the room, you show the first kid that inside the box is actually chewing gum. You put the chewing gum away back in the “Chalk” box, and then ask the kid, “If I showed Sally-Anne this box, what would she think was in it?” The obvious answer to an adult is chalk, because Sally-Anne has not been shown the secret. But to children who have yet to have the breakthrough of insight I am talking about here, they will say “chewing-gum”, because they can’t understand that other people don’t necessarily know everything they know.
I suspect that related to this idea is the idea of object permanence - if, to a sufficiently young child, you show them an object, and then put it behind your back, the child thinks the object has disappeared - they don’t realise that one of the properties of objects is permanence, and that it has simply moved somewhere else. This is why playing peekaboo with very small children is such fun - to them, you keep re-appearing as if by magic.
As I say, I suspect these issues may be at least in part behind the idea that your daughter can’t quite understand why Milo and Otis aren’t always in the same place all the time.
As for anecdotes, my daughter used to be a mangler of language. She called licorice “liquid”. She blurred the phrases “pulling my leg” and “winding me up” so that if you were teasing her, she would say “You’re winding my leg up!”
I kind of liked the imagery of the last one. Still use it.
When my friend’s son, who’s now a teenager, was little, he bit off the end of some string cheese, and when it fell apart, wanted his daddy to tape it back together. 
Wow. Just had a take me back moment while reading a book with dual timelines and vaguely remember back to when I had the same experience of not understanding the concept. And also remembered this thread about it which alerted me to recognizing that.
I haven’t finished reading the thread, but that reminded me of my kids trying to come to terms with the fact that mommy and daddy also had mommies and daddies.
I mean they knew two grandmas and a pop (my dad) but it didn’t occur to them that they were the mommies and daddy of mommy and daddy.
I was substitute teaching a third grade class (kids around 8) and happened to mention my father, which staggered them. How could I, an adult, have a parent? I asked if any of them had grandparents. Oh, yes. It turned out they thought grandparents were “Mommy and Daddy’s friends.” I explained they were Mommy and Daddy’s parents. They didn’t believe me, and all agreed to check when they got home–some were babysat by grandparents. Wish I could’ve been there the next day.
One girl wanted to know if my mother made me do all the work and wouldn’t let me go to the ball. I think she was conflating me with Cinderella, an adult with a (step)mother.
When our son was a baby, my husband often held him up to a mirror, and when I came up behind them one day, our son turned around, because he’d figured out that if Mommy’s in the mirror, she’s nearby.
When he was a little older, I somehow found out that he thought the Pope was the Easter Bunny in disguise. Specifically, the Pope’s high hat–a miter?–was hiding his ears.