There are several synonyms for the term "common axe". A popular term for a common axe is "hand axe". This type of axe is typically used for chopping wood and other materials by hand. Another synonym for a common axe is "hatchet". A hatchet is a small axe with a short handle that can be used for more precise work. The term "chopping axe" is also a synonym for a common axe, as it describes an axe primarily used for chopping tasks. Additionally, the term "firewood axe" can also be used as a synonym for a common axe, as it describes an axe specifically used for cutting wood for fires.