One is a statement about a single instant. The other is a statement about what happens over the next several seconds — and they can disagree.
It sounds like a contradiction the first time you hear it: an aircraft can be correctly, provably "stable" by the textbook definition, and still be one that no pilot would want to fly. That's not a paradox — it's two different questions being asked about two different things. Static stability asks only: right after a disturbance, which way does the aircraft initially try to move? Dynamic stability asks a completely separate question: given that initial tendency, what actually happens over the following seconds, cycle after cycle? An aircraft can answer the first question correctly and the second one catastrophically wrong — and understanding exactly why is one of the more counter-intuitive ideas in flight dynamics.