Market Research = Overview of Category
Market research is done through some agency. It might be useful for designer to be a part of the process.
It provides an overview of the product category. It gives some view about which product is doing well in comparison with others.
It defines important parameters, features, success & failures, trends.
Basically, it tries to connect the sell figure to its appropriateness or probable reason (Why answer?). This gives a guideline for the important factors/parameters that should be considered while designing the product. It can also give some information for a strategic design.
User Research = User & (User-Product-Environment )
I have done a few projects, which went for the good depth.
It is collecting info about users who are/will be associated with the product.
There are various methods to understand the User-Product-Environment relationship & their interactions.
It gives details about the insights, their wants & needs, pain points & opportunities.