Common uses of parenthetical statements are equivalent to
e.g. appositives. This includes elaboration or examples that clarify but don't change the meaning of the larger phrase or sentence they appear in. Many definitions of "parenthetical" or "parenthetical statement" include only this type of use.
There is a less common use of parentheses or brackets in written English where the inclusion or exclusion of the parenthetical content changes the meaning of the sentence, and it is meant to be read as either or both meanings. What is this called?
- [I hope] It is not going to rain.
- I will [pretend to] enjoy this movie.