Bloody Sunday took place in St. Petersburg, Russia in 1905. A group of working-class Russians went to the Tsar's winter palace to peacefully protest against harsh working conditions. They were shot down by soldiers before they could speak to the tsar; many were killed and wounded.
A completely different Bloody Sunday occurred in Northern Ireland in 1972. The mainly Catholic Civil Rights movement were holding a march in Londonderry. British soldiers responded by shooting thirteen unarmed protesters dead, including six minors; another died from the wounds a few months later. Five had been shot in the back. Army vehicles ran over two protesters. The British never punished those responsible and several songs (one by John Lennon, and other by U2) commemorate the tragedy. There is a Christian rock group that dedicates its name to the event, calling themselves “Bloody Sunday.”
It's worth noting that while the events in Londonderry may be the most famous of the many days which have gained the title "Bloody Sunday", it is a title used for several other days during the history of the Irish Conflict.