Phase separation dynamics is studied in a density-matched liquid mixture in the presence of a weak linear concentration gradient. This novel situation enables nucleation and spinodal decomposition to be studied simultaneously. We observe at all quench depths (i) a central zone of nearly constant concentration width where interconnected domains grow linearly with time, surrounded by (ii) a zone of isolated droplets whose width increases with time, with the droplet growth compatible with a 1/3 law. These findings suggest generalized nucleation as the phase separation process.