Heterochromatin spreading, the expansion of repressive chromatin structure from sequence-specific nucleation sites, is critical for stable gene silencing. Spreading re-establishes gene-poor constitutive heterochromatin across cell cycles but can also invade gene-rich euchromatin de novo to steer cell fate decisions. How chromatin context (i.e. euchromatic, heterochromatic) or different nucleation pathways influence heterochromatin spreading remains poorly understood. Previously, we developed a single-cell sensor in fission yeast that can separately record heterochromatic gene silencing at nucleation sequences and distal sites. Here we couple our quantitative assay to a genetic screen to identify genes encoding nuclear factors linked to the regulation of heterochromatin nucleation and the distal spreading of gene silencing. We find that mechanisms underlying gene silencing distal to a nucleation site differ by chromatin context. For example, Clr6 histone deacetylase complexes containing the Fkh2 transcription factor are specifically required for heterochromatin spreading at constitutive sites. Fkh2 recruits Clr6 to nucleation-distal chromatin sites in such contexts. In addition, we find that a number of chromatin remodeling complexes antagonize nucleation-distal gene silencing. Our results separate the regulation of heterochromatic gene silencing at nucleation versus distal sites and show that it is controlled by context-dependent mechanisms. The results of our genetic analysis constitute a broad community resource that will support further analysis of the mechanisms underlying the spread of epigenetic silencing along chromatin.