I HATE how it's confusing..
http://www.everymac.com/images/other_images/nano-sim-sizes.jpg
Mini appears to be "Standard phone-sized SIM" -- so, yes, you're right.
You'll need to buy a new SIM, so
(for some reason I associated "Mini" with "Nano" and got the sizes
backwards since nobody really references the full credit-card size SIM as a
"Standard SIM")