As far as I know all Claris brakes are rim brakes, so yes you would need to buy the brakes independently. Road disc brakes are still relatively newish. Or at least have only recently started to gain traction in the market. I believe Shimano recently released the new version of the 105 line that uses a disc brake. You could look at going that route for the brake but..
Compatibility will come into play with the brifters (brake & shifter) as the Claris is made for 8 speed and the higher levels that include a disc brake will more than likely be 9/10 or 11sp, but it is doable with some creativity or use of other brands/models. If my memory serves me you could use the ST-R500 from Shimano with a mechanical disc, its an 8sp. Personally I don't see a need for disc brakes on a road bike as cantis are tried and true but that's just my opinion.
Also STI in shimano terms stands for Shimano Total Integration , a fancy name for the brake lever and shifter in one unit.. aka a brifter