What's the difference between "take a guess" and "make a guess"? Seems like they're both grammatically correct.
I don't know how old she is, I can only make/take a guess.
As a native speaker, I just want to confirm you are correct. While in my region of the U.S., I hear "take" much more often -- and I don't even know if other regions are different -- I don't think either is any more correct ... perhaps merely a preference. They are not only grammatically/technically correct, but they are also both in broad common use.
So I would call these 100% interchangeable.