This is a great question Yakup. I spend time getting my students to think about these categories along with users. I do not know what context you are thinking about, if any in particular, but the context obviously influences my answer to this. As a general statement I think that consumer is a much broader term than customer where the latter seems to imply more of a contractual relationship between provider and user that need not be present with a consumer. Does this help? Please ask more and we could discuss this.
Following Paul's answer, the context and the type of market of study, such as financial, B2B or baby products, the relationship between customer and consumer can range from weak to strong. Would need more information on research subject.
I believe customer are those who are in direct relationship with supplier. They are the ones who actually buys the goods or services. Consumer are those who consumes the products or services who may not necessarily be a customer. But in the academic literature both the terms have been used interchangeably, for example we always say customer when someone comes to a shop for buying a product and we always say consumer behavior not customer behavior.
A customer can be a consumer (first case) or cannot be a consumer (second case). We can think taking into consideration that buying proccess is one role play, the second one can be a consulting proccess role play or a mix of the two role plays. I make this difference in front of my students and clients, just to underline the diference between buying and/or consuming either direct, either indirect. We can design a matrix that shows all the cases. But, more important, I think is to treat both consumers and customers as prescribing people either for the product or services, either for the image of the product/services, the image of organization, the image of local or regional community where are produced or offered the products/services.
On short, not any client is a final consumer-see importers, exporters or distributors-, but any consumer has the quality of a final consumer, where the final perseptions belong to final consumers; and, not any final consumer has the quality of a customer or a client, as you can eat a cake, but you did not buy your cake, as it was a gift. If, your perception, as a final consumer will be a positive one, maybe you will take the decision to go and buy it for yourself. So, how to take a type of decision, buying or selling role and inluencing perceptions for the customers/clients and for the final consumers (some clients cand can be final consumers or not) can be an improved approach.
A customer is always a consumer but a consumer may not be a customer. A customer may buy something for his or her friends or relatives but he or she needs to consume some level of service required to obtain the products or services.
A consumer may not be a customer as it they may just simply consume without going through the decision making process. And if they go through the decision making process, then they are also a consumer.
consumer/user is the end user of an organizational product/services while customer is a repeat buyer of same product/brand/outlet in case of products and is referred as clients in case of services. while Buyers can be anyone who purchase the product/service as a point of sale. thus
a buyer can be a consumer as well as customer or simply a buyer
consumer can be a buyer as well as customer or simply a consumer
While consumer is someone who is consuming the product/service
I guess customer has nothing to do with consumer. Surely, for some services, you do not need to be a customer to consume it (e.g. open source product). In the other hand, you do not need to be a consumer to pay a service or product (e.g. charity)
Perhaps, a better question may be: When will an individual take role as a customer? and When will an individual take role as a consumer? (CMIIW)