Actually there are more than 3 groups descendent of the original Hospitallers of Malta. All have historically defensible claims of connection to the pre-Reformation order of Knights or, monks militant, but NOT all are Roman Catholic. One group is connected to the UK, another to Germany, another to, the white Russians (that is the Eastern Orthodox Russian Czar).
In Germany, hospitals, as well as Red Cross functions are funded by Hospitallers using this symbol:
"Recently, the Catholic-sponsored Order (SMOM) took the Ecumenical Order to Court in the U.S. over charges of Trademark violations. The charges were successfully defended and the SMOM charged with fraudulent behaviour during the Application process.
After much dispute and historical analysis, the SMOM was found to have "obtained four of its trademarks by engaging in fraud during the application process", and "ignored the rights of The Florida Priory and its parent international organization". "The court also found that since the two organizations share a common history prior to 1798, references to that history are appropriate and do not constitute false advertising under The Lanham Act."
The Ecumenical Order established a case that they were the unbroken line of the Order, who left Malta and Catholicism after surrendering to Napoleon and found refuge in Russia, whereas the SMOM was re-established under Catholic Auspices in 1834."