Rabbit syphilis isn't the same as snuffles.
Rabbit syphilis, aka vent disease, spirochetosis, or treponematosis, is caused by the spirochete bacterium Treponema paraluis cuniculi, which travels in the blood. It is not a respiratory illness, but is most definitely an std, being passed most often by mating, though contaminated materials can also result in the spread. The rabbit's nose is not usually snotty, rather it can be crusty and scabby because the infection, which produces crusty lesions and scabs around the vent, causes the same to appear around the nose, mouth, eyelids, and sometimes even the feet, when the animal grooms itself and transfers the bacteria to those sites.
On the other hand, snuffles is a common name for pasteurellosis, which is caused by the bacteria Pasteurella multocida, a gram-negative coccobacillus. It produces upper respiratory disease and infections in eyes, ears, nose, bones and internal organs. Symptoms include labored breathing and a characteristic thick white snotty mucous that appears on the nose and often also inside the front legs as the rabbit tries repeatedly to clean its nose. It is a penicillin-sensitive bacterium but many people believe infected rabbits carry and spread it for life, even after treatment. Note, however, that many, perhaps even all, rabbits carry Pasteurella bacteria, but only some individuals contract an infection.
Not all runny noses or respiratory illnesses in rabbits are pasteurellosis, though; while rabbits aren't known to get viral cold infections like humans, nonetheless I can tell you they do get what look like colds, as well as hay fever-like allergies, without having pasteurellosis. The only way to be 100% sure that a rabbit with a snotty nose has pastuerellosis is to get a culture.
