Great comments and summaries already. To those I’ll add:
User research is “steep and deep”: it is highly detailed and granular, and can be used to understand WHY people feel a certain way. Market research (which I define as using quantitative methods like surveys, and looking at large groups) will identify WHAT people feel, but does poorly at the WHY.
User research is directional - it can identify users/areas of interest or trends that are not statisically valid, yet can be used for subsequent statistical validation through market research. If you have the luxury of using both methods: user research identifies potential areas of interest in a specific user group, market research validates the occurance (i.e. “is it large enough to be of interest to us?”) of that user group.
And of course, highly qualitative, deep, observational/ethnographic research (“user research”) is the only research method that can identify unarticulated needs, unmet needs, and under-met needs. It’s almost impossible for quantitative methods (“market research”) to uncover opportunities or to evaluate innovation, because it is extremely difficult for people to evaluate or imagine/invent things that they’ve never seen or experienced.
Market research uses quantitative data (large numbers) and remote tools (surveys, demographic info, sales info, etc.). User research uses qualitative data (small numbers) and local tools (interviews, observation, etc). Both can be done well or poorly. Both can yield helpful information, but they are different methods, yield different information, and require different skills to plan, design and implement. They are complimentary in the best of cases.
If you’ve only got time or budget for one type, the decision of which type depends on
1. newness of the product space
2. amount of information known about the potential users
3. comfort of the development team (and execs) with ambiguity
4. where that ambiguity lies (for instance: the development or manufacturing process vs. potential market vs. ability to merchandise/assort/distribute vs. validity of user need, etcetera)