A blacksmith is a person who works with iron and steel. The blacksmith hammers hot iron on an anvil to change its shape. Blacksmiths make iron and steel tools.
A smith is a person who works in metal. A blacksmith works with iron and steel. A thousand years ago, people only knew about seven metals (iron, gold, silver, copper, tin, lead, and mercury). By color: gold is yellow; copper is red; and silver, tin, lead, and mercury are different gray colors. Iron is also a gray color if you shine it, but usually its surface is covered with a black oxide, which is a kind of rust. This black color forms very fast in a blacksmith's fire. The other metals have light colors, but iron is a dark color, so it is called the black metal in English. A smith who works the black metal is a blacksmith.
A farrier works with iron like a blacksmith. The only ironwork a farrier does is to make horseshoes.