A mnemonic (memory aid) for this:
Are there any letters from “choice” in Balk? No, so there is no choice in a Balk.
Are there any letters from “choice” in Catcher’s Interference (CI)? Obviously. Thus, there is a choice available in CI.
Consider, though, that in the pro game (both uppercase and lowercase), we (umpires) are taught to enforce the penalty of CI, unless it is satisfied by the outcome of the play. We enforce it, and then we allow a manager to inquire about (the) option(s); the managers are paid pros, and the burden is on them to know (the rule). However, in the amateur game, it is best practice to mention that an/the option is available. We should still enforce the penalty first, though, to make the rule’s application innate upon ourselves, but after that enforcement, be accommodating and thorough in discussing the optional outcome. You’ve got plenty of time.
Once you apply the penalties of Balks and CIs, you start to recognize and realize the differences between them.