In the UK we never use cups, only metric (for most recipes nowadays) or imperial measures (pounds, ounces, pints, tablespoons etc.).
Note that the cup measures used in NZ and Australia are slightly different from the ones used in the US, also the Australian tablespoon is bigger than the one used elsewhere.
Generally you are safe enough using metric measures everywhere in the world except the US, where you must use US measures - cups for volumes less than a pint, pounds and ounces for weights. Volume measures would be used for liquids and powders, but also 'flowing' solids such as rice, corn (grains) or sweetcorn niblets; you could imaginably measure chopped mushrooms this way, but certainly not whole ones.
The split between US (conservative) and the rest of the world (metric) applies to some other measures too, not just cooking.