Did you think about this before typing?
Clue: how many countries does an EU-wide law directly apply to? One? Or many?
It is also international in that it applies to EU citizen date no matter which country it is held or processed in.
The GDPR creates some new criminal offences that can be prosecuted through courts without the regulatory authorities being involved in Clauses 162 & 163.
Article 82 allows individuals to sue in court for compensation if breaches of GDPR rules cause harm.
The regulatory activities are on top of this.