The existence of a Safety culture and a Just culture, will depend on the Organisational culture.
A SMS is a legal requirement, but one of the key requirements for a SMS to work, is for there to be a Reporting culture. For there to be a reporting culture, there needs to be active examples of a just culture, otherwise people are too afraid to self-report.
The culture of an organisation comes from the top. The fish rots from the head down. So, what is encouraged and rewarded in the company, what is punished or frowned upon?
If organisational culture is described as "the way we do things around here" its down to what employees see as normal/acceptable behaviour.
If employees are encouraged to adopt a "culture of conscious enquiry" where every employee looks critically at what they do and how they do it, without fear, you have the makings of a great safety culture. Without this attitude, you have an acronym that satisfies a legal requirement,