Both of the orders were founded after the establishment of the Kingdom of Jerusalem, following the First Crusade. The largest difference I know of between the two orders is their stated purposes when they were charted. The Knights Templar were primarily concerned with the protection of the Holy City and protecting pilgrims in the rather dangerous roads leading to Jerusalem. The Knights of the Hospital of St. John were charged with protecting and staffing the Hospital of St. John in Jerusalem. While this really only shows their differences in their early years, it may help you disambiguate between the groups. Sources: The crusades by Thomas F. Madden and The First Crusaders and the Idea of Crusading by Johnathan Riley-Smith.

To add to what wowtoast1 says, a bit; the Templars were also able to essentially act as bankers, a pilgrim could deposit money with a Templar house in London, carry a letter of credit from them to the Middle East for redemption and not have to carry cash. This was one of the reasons they grew quite rich, and why they were looted by Phillip the Fair in 1307, after the Crusader kingdoms were lost.

The Hospitallers , after the fall of Jerusalem and going into the Renaissance, became pirates on Muslim shipping, working from their bases on Rhodes and Malta until the Turks finally captured Rhodes and almost took Malta. Eventually after the Battle of Lepanto, the Mediterraenean was mostly dominated by the Europeans. The Knights of Malta became less important there than the Spanish and French navies, and survive today as a kind of club for Catholic royalty. Desmond Seward: The Monks of War