market: the entities with the interest and means to buy your product
The term "market" is an aggregate concept. It is all the entities, consumers, for example, who might be interested in your product (because they assume it will delight them or solve their problems) who also have the means (financial means, usually) to purchase your product. Understanding markets must be done by finding proxies; the market doesn't have the means to express its pains to you. From a product management perspective, you must infer requirements from the market.
customer: An entity that has bought your product
Customers represent the segment of the market that has purchased your product. It's worth noting that the term "customer" is an aggregate concept referring to a multitude of customer stakeholders, e.g., economic buyer, influencers, end users. You can actually talk to customers and they, unlike markets, are capable of expressing their requirements and other desires. Communicating with customers, while itself challenging at times, is a much more straight-forward affair than divining the desires of a market.
So where do I see folks getting confused? Well-known examples include the traditional Venn diagram showing that PM lies at the intersection of customers, technology, and business. I would say that substituting "markets" for "customers" in this diagram makes much more sense. The Business Model Canvas also seems to confuse them. It defines a building block called "Customer Segments", for example. While it may be beneficial to segment your customers, I would say segmenting markets makes a lot more sense when you're fleshing out a business model.
The third case of confusion is a bit more subtle. I've worked with companies with significant market share, i.e., their customers comprise a large percentage of their market. In these cases, it is common for product managers to engage deeply with their customers at the expense of gaining an understanding of the broader market. This tendency is understandable but can hinder growth beyond your customer base, generating a type of chasm for even mature products.
I would say inferring the desires of a market is one of a PMs most challenging tasks. Although you can always try to validate your hypothesis, markets are, by their nature, unpredictable and often full of surprises. My challenge to the PM community is to think deeply about the distinctions between these two concepts and, as importantly, to stop conflating or confusing them.
What do you think? Are my definitions inline with yours? Have you seen people confuse these terms?
UPDATE: Began reading Blank's "The Four Steps to the Epiphany" and it becomes a bit clearer how these concepts get confused: "Broadly speaking, Customer Discovery focuses on testing whether a company’s business model is correct, specifically focused on whether the product solves customer problems and needs (this match of product features and customers is called Product/Market fit.)". I think the point is valid, but talking about customers and calling it "market fit" may not be the clearest way to express the idea.
