There are two styles of minigames used for Crafting: Matching and Making.
Matching minigames use the same minigame you are already familiar with from Harvesting and Mining to assemble the product. Forging recipes use the Matching minigame. Higher level recipes with higher difficulty use smaller and oddly-shaped game grids to make the Matching harder, and have higher goals for bonuses.
Making minigames use a series of tasks to perform the steps required to create the product. Cooking and Smelting recipes use Making minigames. Higher level recipes with higher difficulty have higher goals for bonuses.