@Niner Thanks for your comments. My ascending valve Bb/C trumpet plays, feels, and sounds like a trumpet.
My comments about cornets apply to the "traditional" BBB cornet, and do not necessarily apply to the various "A" series Conns, or similar models from other manufacturers. The acid test I use when I am defining the 2 instruments is:
Is the "Trumpet" an acceptable instrument in all trumpet inclusive ensembles.
Is the "Cornet" an acceptable instrument in serious British Brass Band ensembles.