They both deliver internet services to your home, they just use different technologies.
The nbn network uses optical fibre plus coaxial cable, copper and other technologies to connect your home to fast, reliable internet.
Broadband, or cable internet uses coaxial cable to connect your home to the internet. Depending on where you live it may be your best option until the nbn reaches your area.
(ADSL is different again - it uses your existing copper phone line to deliver internet and a phone service to your home, when the nbn network and cable are not available.)