Questions about speciation of flora can be complex and are so in the case of trillium. A straightforward answer is “yes,” white and red trillium are different species with distinct characteristics, as can be seen from the first photograph.
The white trillium below are in the species Trillium grandiflorum as evidenced by coloration, the shapes of the flower petals and anthers. For this discussion I will focus on the flower petal shape and coloration. The grandiflorum petals are broad at the base and wavy, compared to the more blade-like red trillium, Trillium erectum, straight-edged petals.
There is the obvious difference of color, but Trillium erectum has a white form, not seen here.
Click any photograph for a larger view.
Then, there is this specimen, below, with a stippling of red on blade-like petals with wavy edges. Here is where the experts differ and, in summary, many believe trillium species are an interrelated complex with the possibility of hybridization, sharing of genetic material between the different species to produce fertile offspring. This specimen may be an example of this hybridization.