Is there any difference between road and mtb discs?
The specific word you need is 'rotor'. If you search for 'Shimano 105 disc brakes' you tend to get the calipers rather than the rotor (which is confusingly actually the 'disc' part).

The latest 105 series rotor part name is SM-RT70. See the Shimano 105 series page. 

There will be other rotors that are compatible with 105 calipers, in case you need a 6-bolt rather than a center lock version.

Calipers don't come with rotors because different sizes are required for different applications or preferences.