Ive been doing bronze welding on steel and cast components for the last 50 years and the name still is bronze welding.
Yes, there is bronze brazing and there is bronze welding. The difference between the two is well described in Lancaster, J.F. – “The Metallurgy of Welding, Brazing and Soldering”, George Allen and Unwin Ltd., 1965.
On whether in brazing and soldering there is any fusion going on, Lancaster states:
”In brazing and soldering there is almost invariably some degree of intersolubility between solder and parent metal, and consequently there is interdiffusion at the parent metal surface.”
Chapter V, Brazing, Soldering and Adhesive Jointing, p.122.