CARINET is the standard TMC message database (look at it with a hex editor - you'll see the messages in all 6 languages)

I am not sure if it also includes the location database - I think not

carindb is the map file, with all map data, poi data, and I think the TMC location code database.

So actually with your CD it is not easy to tell if it supports TMC.

But: if the NAV system shows TMC in red then the TMC is not working, mainly because you don't have TMC support on the disc.

And anyway, you always have the issue of encrypted data in Australia...