I would only add one point. Many people use the ™ mark even when the mark itself is registered in the United States and they are thus legally permitted to use the registered mark: ®.

One reason is that an issue can sometimes arise in the international context when using the registered trademark symbol on products or advertising materials. For example: if you are exporting a product to a country that is marked [YourTrademark®] and you have not, in fact, registered your mark in that country, you run the risk of violating their trademark laws, even though you are complying with US laws.

And I suppose that makes sense, as the converse is also true. A foreign company cannot register their trademark abroad (e.g., Romania or Australia) and then use that foreign registry as the basis for marking products sold in the United States with the ® designation.