Let's say we have a $k$ group scheme $G$ acting on a $k$ scheme $X$, we can consider its quotient in the category of stacks, the usual definition of it would be the quotient stack $[X/G]$ defined by
$[X/G](S)$ is the groupoid of $G$ bundles over $S$ together an equivariant maps to $X$.
My Question 1 is why don't we take the categorical quotient?
I think the categorical quotient exists because we can take the categorical quotient in the categories of 2-functors from Schemes to Groupoids, and then sheafify (stackify).
I understand that the stack quotients enjoy some very good properties, e.g. it makes every action look like a free action and it the theory of sheaves downstair is equivalent to the theory of sheaves.
but why people (or do they) don't study categorical quotient as well?
My Question 2 is how do stack quotients differentiate from categorical quotients?
Stack quotient is equal to the categorical quotient in the case free action, and I have the feeling that the two notions agree only when the action is free, is it true?
Thank you very much!