The TM symbol is used for unregistered trade marks and the ® symbol can only be used for registered trade marks.
If you have registered your trade mark, then you own that trade mark and you can order anyone else to stop using it, or any deceptively similar variation of the trade mark.
Using the registered trade mark symbol ® on an unregistered trade mark is an offence under section 151(1) of the Trade Marks Act 1995 (Cth). The offender may be fined up to 60 penalty units, which is currently up to $12,600 (Crimes Act 1914 (Cth) s4AA(1), Crimes Amendment (Penalty Unit) Act 2017 (Cth) s1).
Where an owner of an overseas registered trademark wishes to use their trademark in Australia, they may use the registered trademark symbol ® provided the country of registration is displayed close to the symbol (Trade Marks Act 1995 (Cth) s151(5).
The TM symbol is used to indicate to other traders that you’re claiming rights to trade mark, even if it is not yet registered. However, you won't have the rights to enforce an unregistered trade mark as easily as a registered trade mark. You would have to argue that third parties who use an identical or deceptively similar mark are trying to pass themselves off as your business, or pass their products off as your products (i.e. as "counterfeit" goods). Proving that you've got a reputation to pass off can cost on the order of $50,000 or more in a court action. That's not necessary for a court action involving a registered trade mark.
You can apply to register your trade mark if you have used the trade mark in Australia before anyone else; or you have applied for registration before anyone else, and have created the trade mark with the intention to use it.