According to Texas A&M Plant Answers, there are several varieties of cress:
...such as Garden Cress or Pepper-grass (Lepidium sativum), Upland or Winter cress (Barbarea vernapraecox) , Bitter-cress (Cardamine pratensis), Indian-cress (another name for nasturtium) or Tropaeolum majus, Penny cress or species of Thlaspi, rock-cress or species of Arabis, Stone-cress or genus Aethionema and Wart-cress or species of Coronopus.Incidentally that Texas A&M page manages to sneak in terribly specific generalizations about the culinary practices of people who live on the east coast, and also "Chinese" [sic]. Which is enough to make me want to question their curiously prosaic description of cress growing conditions:
Water-cress is a hardy, perennial, European herb (Nasturtium officinale) which grows naturally in wet soil along and in spring brooks, dithces and pond margins and is cultivated under such condition for use as a garnish and a piquant salad.
Preparing cress for use in salads generally requires removing the leaves from the stems. As the photos may suggest, when cooking for more than a handful of people, this can be both tedious and relatively expensive. Consequently, arugula tends to be the weapon of choice when peppery greens are called for here at consumptive HQ.