Continuum fallacy (also known as the fallacy of grey) is a logical fallacy which erroneously reject a vague claim simply because it is not as precise as one would like it to be. Vagueness alone does not necessarily imply invalidity.
Specifically, it is the fallacy of assuming that the existence of a continuum of possible states between two different positions means that said positions are not meaningfully different.
The alternative name "fallacy of grey" comes from the assertion that complex, real world decisions and events are never actually "black and white", but consist of "shades of grey" — the corollary to this being that by picking "shades", you've replaced two positions (colours), black or white, with just one colour; grey. Yet some things can be very, very dark shades of grey, and others can be very, very light shades of grey. The fallacy, therefore, is to assume that there is no difference.
The continuum fallacy is routinely committed by race denialists. See, for example, Arguments regarding the existence of races: Continuous change of genetics and characteristics?