Yes, that is what I am trying to say.
In terms of actual EU courts, we have the EU General Court, but that only has competence to hear cases against the EU itself. For example, if the European Patent Office refuses to grant your patent application, you can go there to appeal your decision, or if the EU competition authority thinks you are behaving in an anti-competitive manner, you will face trial in that court.
Most other cases involving EU law are heard in national courts, with the European Court of Justice as the final court of appeal. Generally speaking, judgements in national courts are binding only in that country, but persuasive elsewhere in the EU. ECJ judgements are binding in the whole of the EU. The exception is cases involving copyrights, patents, trademarks and registered designs (known as design patents in the US). For those cases, the national court sits as an EU court, and judgements are binding throughout the EU. Another exception is the EU small claims procedure, where consumers can take cases against suppliers in other EU countries in their local court, and the local court will work the the court local to the supplier to sort out the dispute. Small claims cases are not legally binding, but can be appealed to the European Court of Justice, who's judgements are legally binding.