2 Meanings of Dramatic Climax

In Freytag's theory of dramatic structure, the "climax" is the "turning point" which occurs in the middle of the play. A lot of people are taught this chart in school:

But this isn't actually how the word is used nowadays. Nowadays a "climax" comes right before the end - it's the "final showdown". The visual diagram for a 2-act play is drawn more like this:

Partly, this is semantics. Partly, it's a different idea of what is important in analyzing a story. I had a professor in college who was very keen on finding the middle-of-the-story turning point, where events subtly began to change direction.

I'm not sure how you apply Freytag's diagram to a standard contemporary 2-act play, because it seems like it would land around the end of Act I or beginning of Act II.

Trying to agree on terms
can be like herding worms.