I am told the root is called a chord and I am also told the root is called a diameter
I believe it is a chordal dimension and the true diameter would need a multiplier to be called a diameter
One can make either a chordal measurement for tooth thickness or tooth gap or make an arc measurement; chordal thickness/wdith is far easier. It is unfamiliar to me to call anything having to do with the root a chord.
The root is also associated with a diameter. For an odd-numbered toothed gear one typically makes a correction when the measurement is to be made with calipers.