Without going into too much technical and making speeches that the "common man" like me would not understand, I will try to explain as simply as possible putting myself in the shoes of an ordinary person who wants an answer as simple and comprehensive as possible.
The difference is enormous and substantially is that the TIG melts the metals to be joined while the fillet brazed "paste" them with the addition of a metal alloy with a lower melting point.
In the latter there are two further options for conjunctions: frame with or without conjunctions.
Having said this, the question arises of the passionate cyclist: What is the best method among the three?
We analyze the different methods and draw conclusions. Nowadays the new alloys of steel have exceptional breaking loads and then the companies
that produce pipes for cycling use can produce pipes with very thin, less than half a millimeter and by appropriate heat treatments can withstand high stresses in an arch of time very long (something unthinkable with alluminium frames or carbon).
The fillet brazed being a "bonding" does not melt the metals to be joined so does not alter the balance or at least it does so in a much lesser extent, this depends on the type of alloy / material used to join pipes.
The alloys are commonly used with silver percentage ranging from 5% (the most used) up to 60% of silver (the least used), then temperatures ranging from 850 ° C to about 550 ° C. The higher the percentage of silver less is the temperature of "bonding" and less stress goes to the tubes but more stress to the pocket being very expensive.
Few artisans using alloys with 50-60% silver and advertise their method with the words "Silver Fillet Brazed".
I conclude with the pros and cons.
Pros: ease of processing, cleaning, lightness, freedom of geometries.
Cons: possible breakage of tubes with very thin thickness.
Frame fillet brazed. without conjunctions
Pro: stiffer than TIG, does not alter the balance of the tubes, pleasing to the eye (looks like a monocoque), freedom of geometries such as tig.
Cons: slow processing, more expensive, a few tens of grams heavier.
Frame fillet brazed, with conjunctions
Pro: undisputed retro charm with conjunctions worked and chrome
Cons: slow processing, more expensive, constrained in the choice of the angles.