A “profit centre” in Peter Drucker’s argot, is a department that designed directly to bring in revenue, thereby — at least whenever revenues outstrip the costs of attaining them — increasing the “bottom line”. To be contrasted with a cost centre, but not a waste centre. Profit centres can, and usually are, also waste centres.
A “cost center” in a firm is a department that does not directly earn revenue but still costs money to operate. Cost centers therefore only contribute to profitability indirectly, by enabling profit centres to operate, helping them operate better, and preventing money made by profit centres being lost again. Cost centres may be, and usually are, also waste centres, but that is not to say cost and waste centres are the same: to confuse them is to make the fundamental mistake of modern management.
There is no definition of a “waste centre” in Peter Drucker’s universe, and if you Google it you are likely to land on an undertaking for recycling refrigerators and making landfill. This is because the JC made the term up, in honour of Taiichi Ohno’s seven wastes. Any part of your organisation can be a waste centre; unless your organisation is run with a Toyota-like commitment to jidoka — “automation with a human touch” — every one will be: a place where unnecessary guff happens, out of a surfeit of pedantry, caution, bad analysis, or opportunities to extract rent. Usually, though, the further away one is from measurable revenue generation one’s department is, the more wasteful it will be. It is easy to measure the value of a salesperson: generated revenues. But the value of an inhouse legal team? That’s a subject fit for its own essay.