A marketing-driven organization is run by the Marketing department. It revolves around what marketers do.
A market-driven organization is driven by what the market wants, regardless of what the marketing department feels like doing.
(And of course, there are organizations driven by Sales, by Shareholder Relations and by Operations and Tech too. Even a few that seem to be run by the Employee-happiness Department. Not many, though. Even in these organizations, the option remains: you can be market driven instead. The first step is to choose your market...)