I will be in Australia for 3 days before I fly to New Zealand. Do I need a tourist visa for both countries?
They are 2 different countries and what visa you require for each all depends on what country you are from.
If you are from a 'visa-waiver country' you don't need to apply for a visa beforehand. You simply turn up with proof of onward travel and proof that you have enough funds to maintain your trip in NZ. You will be issued a visa on arrival.
The list of visa-waiver countries is here: http://glossary.immigration.govt.nz/visafreecountries.htm
If you are not from one of these countries you will have to apply for a NZ tourist visa
Australia has a number of options. The easiest are online electronic visas.
Here is a list for the eVisitor visa: http://www.immi.gov.au/visitors/tourist/evisitor/eligibility.htm
The list for an ETA is:
If you are not eligible in either list, then you will have to apply for one
All of these visas allow stays of up to 3 months. The Aussie e-visas are usually valid for 1 year, and for multiple entry.
It will certainly depend on where you're from as to whether you need a visa - some countries don't need visas to visit either.
However, assuming you need visas, then yes, you need two separate visas. They are not the same country, and while there are some reciprocal agreements for some citizens (I'm a NZer and can work visa-free in Australia), for foreigners you'll definitely consider them separate. Different governments, different currencies, different sports teams, very different countries, even if some people struggle to tell the accents apart :)
Fun fact: even New Zealanders need a visa for Australia if they arrive by sea - due to a legacy law.