I've never heard of "electric fusion welding." that isn't a technical term.
"Fusion welding" is a general term. It doesn't refer to any specific "welding process." It refers to ANY process that joins two metal parts together by melting the edges of the joint until the melted regions coalesce and fuse, then allows the melted areas to cool, forming a single piece. There are a large number of welding processes that fit in the category of "fusion welding."
Most arc welding processes make use of fusion welding. Or rather the arc is used to create a fusion weld. In most cases of arc welding a filler metal with the same composition as the two parts is used to bridge any gaps, and to provide reinforcement to the welded joint. Examples of fusion welding processes that use an electrical arc are "Gas-Metal-Arc Welding (GMAW) a.k.a. MIG, and "Shielded Metal Arc Welding" (SMAW) which is also known informally as "stick" welding. Another process is "Tungsten Inert Gas" welding (TIG)
There are other welding processes that don't qualify as "fusion" welding, because they don't physically melt the base material. For example, "solid-state welding" which doesn't heat the two parts above their melting points. An example of a solid state welding process is "friction welding" which is used to joint pipes and shafts. Then there's "soldering" and/or "brazing," which uses filler metals that have a lower melting point than the two parts. This is similar to using hot glue.