The two visas are the ETA visa, which allow you to stay for up to three months, and the Tourist visa, which allows you to stay three, six or 12 months. Both can be applied for online.
The Electronic Travel Authorization (ETA) visa is valid for a year but, as mentioned above, only allows you to stay in Australia for up to three months. The ETA visa cannot be extended from within Australia but can be extended from outside the country.
With a Tourist visa, if you are staying three months and want to extend your stay, you can do that within the country. You can also use this visa if you are planning to study for three months or less.
Depending on the purpose or length of your stay, and your country of origin, the Australian immigration authorities may require you to submit to a health exam or background check prior to issuing the visa. Country of origin is not an issue for U.S. citizens, but a health exam can be required if you have a significant medical condition, or depending on how long you intend to stay or other special circumstances of your stay (see references). If you have major health problems, you may be required to prove you have private insurance for your trip.
If you apply online for either visa, be sure to enter the number of the passport you will be travelling on. The visa is linked electronically to that number. If you lose your passport before your trip and must replace it, you must re-apply for the visa.
