Fusion (fusion welding) is a material joining process for a permanent combining of two (or more) metal pieces that involves melting of a filler material such as a consumable electrode or a wire fed into the weld pool. Fusion occurs when you have atomic bonding of the metal pieces. The molecules of each separate piece of metal and the consumable electrode (filler metal) bond together. This occurs with arc welding such that the atoms of each piece of metal bond together with shared electrons to solidify and become one homogeneous piece of metal.
Penetration (depth of fusion) is the distance that fusion extends into the base metal or previous pass from the surface melted during welding. A full or complete penetration weld can be a really thick weld that has been beveled and then penetrated by being filled with multiple weld passes.