Before the Internet, Americans called the brass rods an the British called them bronze.
No difference.
Since the internet, bronze has become popular as the “correct” term.
Low fuming bronze is recommended for bronze / brass brazing of bicycles.
Nickel-silver rods have no silver, but are silver in color.
Nickel-silver is 9 to 10 percent nickel.
If built up too thickly, such as thick fillets, nickel-silver can become brittle and prone to cracking.
Nickel-silver is for use when brazed joints are exposed to abrasive wear and really have no application in bicycle brazing and it is difficult to to polish.
In America there is low fuming bronze with 2 percent nickel available and is meant for brazing high carbon iron.
It has limited availability in Europe, as the European industry considers regular bronze to be suitable for brazing high carbon iron.
Some frame builders like the 2 percent nickel low fuming bronze as it wets out well and it does not become brittle like 9-10% nickel-silver can.
For bronze brazing of bikes, it is recommended to stick with low fuming bronze.
“Naval brass / bronze” is not low fuming and it not as strong as low fuming bronze, though it is softer and easier to polish.
It was common in old mild steel city bikes in Europe, years ago.
Low fuming bronze is easier to polish than nickel-silver, as nickel-silver is made to resist abrasion.
When chrome moly steel tubing gets “too hot” the copper in bronze brazing can get into the grain of the chrome moly steel tubing and cause it to crack later, when cold.
Nickel-silver has an even higher melting temperature than low fuming bronze.
I’m retired and in America now, but I built frames in Italy from 1987 to 2015.
The air hardening tubing calls for bronze brazing and not silver brazing, as the high temperature of bronze brazing hardens the steel.
The best method to not overheat chrome moly steel tubing is to use a hot torch and heat quickly, but it takes practice.
Thicker tubing is easier to braze than thinner tubing, so it is easiest to learn with thicker tubes.
To me, “brass” and “bronze” brazing rods are the same thing.
When I first started brazing in school in the 1970’s, I only heard it called brass.
If you get low fuming bronze or low fuming brass, you’ve got the right stuff.
The thinner rods are easiest to use.