I just had a very similar conversation, and want to share the thoughts here for everyone's comment:
Market research and UX research are fundamentally different, yet have some overlap. Both are invaluable in their own context, but can easily compliment the other.
Market research is primarily about understanding what people will buy. This is useful in the early strategy and planning phases, and when validating designs/concepts. Market research focusses on large samples that must be statistically balanced to give confidence to decision makers. It also tends to give more weight to attitudinal data (what people say about themselves) rather than on specific behaviours in a certain context. It is about broad, generalised information to help steer how a business meets its customers, and how its customers make purchase decisions, how the brand is understood. It's priority is improving the bottom line by understanding customers.
UX research is almost the exact opposite. It's not about markets, trends, segments, demographics, and less about attitudinal responses. Instead, it looks at how people feel about using a product or service. It is not about generalised data—it's about very specific, deep-dive information regarding users and their contexts. UX research is valuable for providing direction about how a solution should be designed, and how it meets the needs of users. Sample sizes are much smaller because we're not dealing with quantitative data that needs statistical accuracy. We're looking more at qualitative data about what is behind what people say, about what they literally do when given decisions in an interface. Its priority is to improve the user experience, which translates into improved bottom line.
The two should not be confused, but can be combined for good effect. Market research can be used for initial market sizing, analyzing competition, getting an idea about trends and product/service areas that people are interested in, and also for identifying approximate price points. From that initial research, user experience research will dive into the focus area we want to understand more deeply, and which may lead to insights useful for innovation, specific design choices and iterations of a product idea. Once that is done, market research again plays a critical role in evaluating which of these concepts are most likely to sell successfully.
I can recommend Jeff Sauro's nifty summary of outcomes and hows/tasks/inputs across this market-research-to-UX-research spectrum too: http://www.measuringu.com/blog/ux-market-research.php