European law includes legislation and judgments from both EU institutions and Europe-wide institutions. The European Commission is responsible for EU legislation and the European Court of Justice and the General Court is responsible for hearing EU cases. The European Court of Human Rights hears cases from any of the 47 European countries in the Council of Europe including the UK. Remember that this court is NOT a European Union institution.
EU cases often have long titles which is why they look so complicated. But the format is straightforward.