Under the Development Act 1993 (Development Regulations 2008) a 'Significant Tree' is a class of tree within a designated area that has a trunk with a circumference of 2 metres or more or, in the case of trees with multiple trunks, that have trunks with a total circumference of 2 metres or more and average circumference of 625 millimetres or more, measured at a point 1 metre above natural ground level. The Development Act 1993 works in parallel with the Native Vegetation Act 1991 in areas to which that Act applies (essentially rural areas and vegetated parts of metropolitan Adelaide).
Significant trees can include both native and non-native species. Although you may have an exemption to remove or modify a native tree within 20 metres of your dwelling, you will still need to get approval from your Local Council if that tree meets the set criteria of a 'significant tree'.