the explanation i received a long time ago in grade school was:

commas should be used when you want to combine a sentence with a sentence fragment (i.e. something that’s not a sentence); semicolons should be used when you want to combine a sentence with another sentence, provided both sentences are closely related to each other.

now, i’m sure the actual rule is probably more complicated and nuanced than that, but the above idea has served me well throughout my academic career. i’ve found it helpful for getting an intuition on when they should be used and why.