Dianthus is the scientific name of the genus which includes Sweet William (Dianthus barbatus) (which are what these are), Pink (D. plumarius) and Carnation (D. caryophylla) as well as the Cheddar Pink (D. grationopolitanus) which is wild but rare in Britain, and over 300 other species.
Then to confuse things, people refer to pinks as “Dianthus” ignoring all the other species of Dianthus in the same way as we talk about “Primula”, ignoring cowslip, oxlip, primrose, birds-eye primrose, Scottish primrose, Auricula, all of which are in the genus Primula.