Assuming you're not talking about the board game, then there's a distinction that's relevant in theory but much less so in practice: Governed-assured monopolies and a market-based monopolies, the former is enforced using legalized threats and violence against would-be competitors, leaving the monopolist free to do as he pleases in terms of price, quality, and access to his product, while the latter merely describes a state of affairs in which one competitor does so well that no potential customer, given complete freedom of choice, would buy anywhere else. Thus the market-based monopoly is either nonexistent, very localized, or very short-lived, while government monopolies are essentially the root of all evils ascribed to "Capitalism" even though they're clearly statist or collectivist actions.