After more research, I have learned that the term “cat grass” is quite a loose term. In many websites, cat grass actually includes a large number of young grass species. Common oat, flax, barley, and even catnip (Nepeta cataria) which is not even a grass at all, are called cat grass in many websites.
Moreover, the differences in culture and language have made this even more confusing. While gardening shops in Hong Kong sell wheatgrass as cat grass, which is what I have bought, many online gardening shops of the western countries sell wheatgrass as wheatgrass, and cat grass as other grass species (this is a good example to show the advantage of using botanical names).
In conclusion, what I have bought is wheatgrass. And just like other grass species such as orchard grass (Dactylis glomerata), barley grass, oat grass, and other variety of grasses, wheatgrass makes a good snack for our cats and other pets to munch on.
Here is an informative article explaining the good and bad of cat grass, written by a veterinarian and exotic plant lover, which many cat lovers and pet owners may find helpful.