When we talk about concepts we're referring to the mental ideas and knowledge we possess. For a simple example, we have the concept of BIG or BIGNESS. (BIG is a semantic prime in Natural Semantic Metalanguage, meaning that it is a core concept which can't be broken down into other concepts.)
Models of semantics based on prototype theory argue that prototypes rather than boundaries are the best way to understand how we humans actually reason, while also sometimes providing an effective way to describe the concepts we know. For BIG, prototypical big things would include mountains, elephants, and sky scrapers. Defining something by its prototypes (which NSM argues you don't do for BIG because it's a prime) would mean saying that BIG means "when I think of something that is BIG, I think 'That's like a mountain' or 'That's like an elephant'."
But we use concepts to think about non-prototypical things. We think about big mice, or big ants. But it's important to understand that the concept BIG is not being misused when we think or talk about big ants. It's not limited to its prototypes. Nor is the concept BIG being only metaphorically applied to ants. When an ant is BIG that is still a pure use of the concept of BIG even though it's not prototypical. We might teach a concept through its prototypes, but its meaning is not necessarily truly found in its prototypes.
Similarly, a small star is truly SMALL. I think this shows one last difference between concepts and prototypes: prototypes are identified relative to being a human, but concepts (for adjectives at least) are relative to whatever is 'normal' for the noun.