The persicarias are members of the dock family and include common weeds such as redleg (or redshank as was) and water-pepper. Pale persicaria (Persicaria lapathifolia) is much like these two species but perhaps less common being a lover of rich soils. Indeed, this does not seem to be a common species in Dorset at all, probably because in the heathlands and on the calcareous soils the earth will not be rich enough for it. It also, apparently, is not a good competitor and so would struggle to survive against more dominant heathers and grasses that one would find in these common Dorset environments.
It is a much bushier plant and the flowers are paler cream or white, with just a tinge of pink, compared to the other two and the flowers often tend to droop over under their own weight when fully developed. It lacks the intense red stem that redleg has; a much paler plant in stem and flower hence, as its label implies, 'pale' persicaria.