I don't think there is anything specific in game that spells it out exactly.
From the item description
Quote
A primitive tool useful for cutting wood, mining stone, repairing & upgrading walls, doors & windows. Not the best weapon.
Repair with Small Stone.
Scrap to Small Stone.
Axes Loading screen tip
QuoteAxes are excellent at harvesting wood, but are not the weapon of choice for killing zombies.
Pickaxes Loading screen tip
QuotePickaxes are great for harvesting the various ores such as iron, lead, coal, oil shale and potassium nitrate.
Axes have reduce block damage against earth, stone, and metal
Pickaxes have reduce block damage against wood and earth
Shovels have reduce block damage against wood, stone, and metal.
It follows the logic of using the correct tool for the task at hand. It is going to take a person longer time to chop down a tree with a shovel instead of an axe, a longer time to mine ores with an axe rather than a pickaxe.