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It is gluing, but it helps that the glue is hot enough to also melt the glued materials a little bit.
Soldering and brazing really are pretty much gluing, though. Fancy hot glue metal with fine tuned properties for penetration and beading.
Which is why most glues are really agressive towards the surfaces they adhere. Better bonding if it melts a littke into each other and then hardens together.
The glue is the melted metal of the pieces being glued.
Almost never.
You can do it but usually you feed in wire or a rod.