The Silence is a name for a an 'order' or 'movement', it seems obvious that the creatures that are often reffered to as 'The Silence' are a separate species themselves (possibly with a different name).
Well, the Slitheen aren't a species, they're a family. The French aren't a species, they're a nation. And so on.
I believe the term "Silence" is used for the order/movement, while "Silents/Silent" is for the species.
I actually was JUST looking at this page (http://tardis.wikia.com/wiki/Silent), likening Slenderman to their kind in a post on 4chan. The Silents is the race, while The Silence is the 'religious order' mentioned by The Tesselctor (The ship operated by the time cops in "Let's Kill Hitler" and "The Wedding of River Song"). Phonetically they sound the same, so I was confused too, but a quick search on 'Silence' mentioned 'did you mean Silents?'