Almost, SAW is a version of EFW. It could also be GTAW, GMAW, Plasma, Laser, or a few others as long as you actually melt the metal.
SAW can be done poorly (as any method can) and some people don't like it so they place limitations on it. It can be prone to higher inclusion content.
ERW does not actually melt the metal, you get it hot and plastic and squeeze it together.
EFW without filler is Autogenous welding, or you can add filler
SAW is by definition with filler.
In their EFW section do they mention filler?
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P.E. Metallurgy, consulting work welcomed