I had a conversation with my pharmacist about this recently and you are essentially correct.

The active drug is identical, but the material used to make may be different and the coating may be different also. So a branded off the shelf tablet may, due to how it's made and the extra markup (Xofen Xtreme Pain relief) get to work 5-10 minutes before the generic version, or it may taste sweeter and be easier to swallow for children, be in gel form etc.

It's worth noting that this is different from the types in the article - https://www.accc.gov.au/media-release/court-finds-nurofen-ma... where products like Nurofen Period pain and Nurofen Migrane were the exact same thing.