Quick answer
People use the words interchangeably, but technically a wire is a single conductor (one strand or a bundle of strands acting as one), while a cable is two or more insulated conductors grouped together, usually under a common outer sheath.
So the single-core house wires you pull through conduit are 'wires', whereas a multi-core product that carries live, neutral and earth together in one jacket is a 'cable'. Both carry electricity; the difference is construction and how they are used.
In everyday Indian usage 'house wire' simply means the single-core building wire used for home wiring. If you are unsure which you need, see how to choose the right cable.