A video I saw said the C note above middle C (octave) is called Treble C. Below middle C is called Bass C. He didn't mention other notes. Would the same be true referring to the D note on the treble staff as treble D? I assume ALL the treble notes E thru F are called treble notes and same for bass notes. Is that the correct music terminology? And any notes above the treble staff are called high C, high D and below the bass staff is low C, low D, etc.? Something isn't right because there are 2 D notes above middle C. They wouldn't both be treble D.
The only way to really be clear about what pitch is intended is to use a system that indicates the octave like Helmholtz or Scientific Pitch Notation.
'Names' can be unclear. 'Middle C' has a clear meaning, it's
C4. But names like 'high C' aren't clear. For a soprano a high C is
C6, but for a tenor it is
This wiki chart shows a combination of octave naming.