Magnetic materials — iron, steel, nickel and cobalt. Most substances, including copper, aluminium, plastic and wood, are not magnetic at all.
Note that not all metals are magnetic. A copper coin is not attracted to a magnet, and this is a quick way to tell steel from aluminium in the laboratory.
Induced magnetism — a magnetic material becomes a magnet when it is placed in a magnetic field.
This explains why a magnet attracts an unmagnetised iron nail. The nail is not a magnet to begin with, but the field induces poles in it, arranged so that the near end becomes the opposite pole to the one attracting it. Unlike poles attract, so the nail is pulled in.
Attraction and repulsion are not equally useful as tests. A magnet attracts both another magnet and an unmagnetised magnetic material. Only repulsion proves that something is itself a magnet, because an unmagnetised material can never be repelled. This is the standard examination question and the answer is always repulsion.
Magnetically hard and soft:
Magnetically hard — difficult to magnetise, but keeps its magnetism once magnetised. Steel is the example. Used for permanent magnets: fridge magnets, compass needles, loudspeaker magnets.
Magnetically soft — easy to magnetise, but loses its magnetism as soon as the field is removed. Iron is the example. Used for electromagnet cores and transformer cores, where the magnetism must switch off the moment the current does.
The words are nothing to do with physical hardness. Soft iron is still a hard metal.
Choosing between them. An electromagnet in a scrapyard crane must drop the car when the current stops, so its core is soft iron. A compass needle must stay magnetised for years, so it is steel. Swapping the two materials would give a crane that never let go and a compass that forgot which way was north.
Example: a chain of paper clips hangs from a magnet. Each clip has magnetism induced in it and becomes a temporary magnet, inducing magnetism in the next. Remove the magnet and the chain falls apart, because steel paper clips retain only a little magnetism.