student wrote: Kat will say something or Kat said that... both point toward primarily toward what Kat is doing. Tell points more towards the content of the speech (i.e., the direct object). For example, Kat will tell a story
Yes Kat can tell a story but she can also tell me something or say something to me.
Tell + story is just a colocation, for me it has nothing to do with meaning.
Tell someone something and say something to someone are the same in every way other than this grammar difference with direct and indirect object... say requiring "to" and tell not.
Kat will tell some random words .
Again to me it's just colocation, grammar of habbit and not of meaning or nuance.
Just the same as we say "light" a cigarette not "start" a cigarette. or "ignite" a cigarette, it's just a collocation.
another example you can say extremely happy but not highly happy. Just habit dictating what sounds write and wrong, not meaning.