In soldering you melt only the soldering material (not the pieces you want to join) and when it solidifies it holds the 2 parts together (adhesion to each on of them). 
In welding you melt (at the joint !) all 3 partisipants: The 2 metals and the welding rod..... a "pool" of molten metal is created and upon colling it creates a welding strongly hold togethr. 
Soldering is performed generally in a much lower temperature than welding, and the "bond" is much stronger in welding.  Please note that not all metals weld together.