In a binary context True and Not False are the same. But most of the world is not binary.

I had a disagreement with my father when I was about 5 years old. I said “I don’t think so!” about something - I don’t recall what. Something fairly trivial like “Is your brother down there with you?” He corrected me “You should say ‘I think not’”, as he often did when I said “I don’t think so.”. His English English was different from my Canadian English. I thought about it briefly and replied: “You’re wrong. ‘I don’t think so’ and ‘I think not’ are different. I don’t think ‘not’ so it would be wrong for me to say ‘I think not’. I don’t have any opinion about it. I don’t know. I didn’t think about it at all until you asked me. And I still don’t know. I just don’t think so.”

He conceded to my 5 year old logic. And I stand by it to this day.

Of course, many people use phrases that literally mean one thing when they actually mean something else. If you’re familiar with them, you might know what they mean despite the literal meaning of what they say.

And you should read Le Ton Beau de Marot before you get too caught up in whether a translation conveys the same meaning as the original.