I think the usual way of defining a millionaire is that it is somebody who on paper has the equivalent of a £million (assuming it is a British millionaire). However, that money may be tied up in a house, cars, business assets, or stocks and shares, and they may not have access to very much in actual cash.

I suppose somebody may appear to be a millionare, but if they traded in all their assets they may not realise a million - it all depends on the value of the assets at that point in time.