The difference is in the acronyms.
PADI - Professional Association of Dive Instructors
SSI - Scuba Schools International
A PADI instructor essentially works on their own (though most work as part of a shop), but SSI instructors must be working under a shop's banner. If you want to buy a whole bunch of your own training gear, your own insurance, and instruct independently on the weekends out of your house, go with PADI. SSI will not allow you to do that. PADI will let you partner with a shop and do it just like SSI requires instructors do, which is to basically be an independent contractor, but you get to use all of the shop's equipment, resources, and, most important, insurance.
I'm an SSI Dive Master right now, and will be starting the ITC soon. As an SSI Dive Guide, you can lead groups of certified divers, but you cannot instruct. Once you get the Dive Master recognition (by taking Science of Diving if you haven't already) you can be an assistant instructor for an Open Water classes (but not an Assistant Open Water Instructor - that's a certification that allows you to teach Scuba Skills Update and Try Scuba). Dive Masters assisting with OW classes are not allowed to do certain skills in the pool, like anything that relates to CESA or turning a student's gas off while underwater, and can only unofficially evaluate a student's skills, but not sign off on mastery. I believe it is the same for PADI DMs when assisting with classes. Dive Guides are also certified snorkeling instructors, so if your shop has students sign up for the snorkeling recognition, you can be the lead instructor and issue cards and earn pro points.