Customer driven innovation means customers looking forward for more innovative product and service , so you have to develope your company to satisfy customers needs . , but customer driven influence means customers lokking forward for brand names and more promoted goods and service in markets .
Customer driven innovation is explained by the phenomenon of co-creation ( ref:CK Prahalad and Venkat Ramaswamy ), where active interaction between organization and customer result in product / service innovation. Customer driven influence, on the other hand, result in brand extensions of the same product / service, depending on the preferences of target customers of particular market segment.
The difference is not very easy to define. I believe that customer influence leads to innovation. In other words customer driven innovation is about creating new things be it products, services or processes. The concept of co-creation is certainly very relevant here. On the other hand, customer influence is any type of effect a customer has on a firm through info or suggestions or through the experience of customer service. So, I think that customer influence leads to customer driven innovation, it makes it possible if the company is customer-oriented and aims to work with customers and learn from customers.