Home-made describes food or items someone makes in their own home rather than buying — a home-made cake is baked at home. Handmade focuses on the making process itself, using hand tools rather than machines, and the item might be sold by a craftsperson (a handmade leather wallet). Home-cooked is narrower — only used for meals prepared at home (a home-cooked dinner). DIY (do-it-yourself) is broader still: it covers any project done by the owner rather than a professional (a DIY bookshelf), not necessarily at home. Choose home-made when the key contrast is home versus shop; choose handmade when the contrast is hand versus machine.
Formed by combining 'home' (from Old English hām, meaning 'dwelling place') and 'made' (past participle of 'make', from Old English macian). The compound has been used since the 1600s to describe things produced inside a household rather than by a professional craftsperson or factory. Over time it became especially common for food, gifts, and household items made at home.