No, they actually won't. The Data Protection Directive needed to be implemented by national legislators into national law, but the GDPR is a regulation which means it is directly binding law.
Only a few technical, minor points need to be spelled out in national regulations or laws.
Each country (or state, in the case of Germany I believe) will have their own privacy commissioner with substantial leeway. Now technically these differences won't be implemented as laws, but there will be substantial differences between eg the French and the UK privacy regulators.
The GDPR also allows for individual states to strengthen its provisions, eg for genetic data.
Only a few technical, minor points need to be spelled out in national regulations or laws.