frogman liked all 3 of those Clark Terry clips.
Nat Adderley on the cornet;
(10) Nat Adderley - That's Nat ( Full Album ) - YouTube
(10) HD - Nat Adderley Quintet - The Old Country - YouTube
flugelhorn or cornett?
It is as clear as day that the shape of the bore, irrespective of the instrument, will affect the sound that the instrument produces. If a brass instrument has a conically shaped bore, then the tone of the sound produces is warmer.
However, the instrument will have fewer upper harmonics.
On the other hand, if an instrument has a cylindrically shaped bore, then the tone of the sound it produces is brighter as compared to instruments with a conical-shaped bore.
Additionally, the instrument will have more upper harmonics. The exception to this rule is the horn, otherwise, it is generally applicable to every other instrument.
There is an archaic formula used to describe the shape of the flugelhorn and the cornet respectively. It states that the cornet has a bore that is half-cylindrical and half conical, while the flugelhorn is a third cylindrical and two thirds conical.
Though a bit old-fashioned, this formula gives a slight clue on how the two instruments differ from one another, when it comes to the bore shape and consequentially, the sound the instruments make.
Full article here: Flugelhorn vs. Cornet (What's The Difference?) - Pro Music Vault