Apparently pic related is a thing.
Post math terminology that tripped you up at one point.

fuck math

Is there any difference between both definitions?

P53060
They're different when not all elements are comparable. Pic related from Wikipedia
https://en.wikipedia.org/wiki/Maximal_and_minimal_elements
shows a bunch of numbers with divisibility used for ordering instead of the usual ordering. By this order 1 is smaller than 2 which is smaller than 4, and 1 is smaller than 3, but 3 and 4 are incomparable since neither number is divisible by the other. Under this order both 3 and 4 are maximal elements of the set {1,2,3,4} since neither one has an element greater than it.

This sort of thing comes up more naturally when you're ordering a collection of sets by set inclusion. A maximum would be a set in the collection that has all the others as subsets, whereas a maximal element would just be a set that's not a subset of any of the other sets.

P53054
that was one of the first things i learned outside of grade school math and it never tripped me up because im not a dyslexic autist wigger from my parents overdosing on mayo and febreeze. a maximum has to be related to every other element (which it may not be since its a _partially_ ordered set), and maximal are just the "top elements" of the forest
P53062
literally retarded explanation overly complicated like a typical c++ haskell wigger. just formally defining a poset and giving the two OP gave definitions should be enough. using this as an analogy is autistic, like it doesnt make it any easier, whereas my informal tree shit above _can_ help

basic function notation like [tex: f : \mathbb{R} \to \mathbb{R}] confuzzled the frick outta me in hs

P53076
why are you so angry esl-kun?