What is the difference between Scuba Schools International (SSI) and PADI?

Very little. SSI and PADI are the two largest scuba diver training and certifying agencies in the World. Both agencies are members of the World Recreational Scuba Training Council (WRSTC) and as such, adhere to minimum and recommended scuba diver training standards - with each agency producing their own working Diver Training Standards, whilst remaining within the parameters of the WRSTC umbrella standards. The skills taught are also the same - after all, both agencies are teaching students to become certified as safe confident scuba divers and there's only so many ways this can be achieved.

Both SSI and Padi recognise and accept each others diver certifications, and both agree upon prior recognition of the others diver certifications when a diver signs up to complete onwards training. Meaning, divers may cross over from either agency to the other when they undertake and complete another more advanced diver training course.