The Knights Templar were not the only military order during the Crusades. There were several including the Knights Hospitaller who actually predated the Templars. They ran hospitals, hence the name, before becoming into an armed crusading body.
There is a shadow over the Hospitallers. Because when the Templars were crushed, the Hospitallers benefited by gaining much of their lands and wealth. Doesn’t really seem very sporting of those knights!
Origin of the Hospitallers
The Hospitallers started out running a hospital in Jerusalem with the backing of Italian merchants BEFORE the city had been taken from Saracen control in 1099. They also managed hospitals on the pilgrim routes in modern France and Italy. In the year 1113, they achieved official papal recognition as the Knights Hospitaller.
Once Jerusalem was in crusader hands, the Hospitallers seem to have responded by upping their activity and undergoing something of a transformation.
Maybe in response to the formation of the Knights Templar around 1118, the Hospitallers rapidly militarised. They went from running a medical operation to taking up arms and fighting alongside the crusaders. The order also became more French than Italian influenced.