Consistent with its approach late last year in WorkPac Pty Ltd v Rossato  HCA 23 (4 August 2021) when determining if an employee is a casual or permanent, the High Court upheld the primacy of the contract stating that, “the character of the relationship between the parties in this case was to be determined by reference to the rights and duties created by the written agreement which comprehensively regulated that relationship”.
If the substance and reality of your relationship with a worker does not clearly fall within the confines of how you treat it (i.e. not clearly a casual employee or not clearly an independent contractor), then these decisions emphasise the importance of having in place a comprehensive written contract with your worker which sets out the contractual rights and obligations of the parties.
For completeness, the terms of the written contract do not include the name you give it. The fact that you call it “Independent contractor agreement” or “Casual employment contract”, is of no significance.
If you have any questions, please do not hesitate to contact me.