A confounding aspect of biological ageing is the nature and role of senescent cells. It is unclear whether the three major types of cellular senescence, namely replicative senescence, oncogene-induced senescence and DNA damage-induced senescence are descriptions of the same phenomenon instigated by different sources, or if each of these is distinct, and how they are associated with ageing. Recently, we devised an epigenetic clock with unprecedented accuracy and precision based on very specific DNA methylation changes that occur in function of age. Using primary cells, telomerase-expressing cells and oncogene-expressing cells of the same genetic background, we show that induction of replicative senescence (RS) and oncogene-induced senescence (OIS) are accompanied by ageing of the cell. However, senescence induced by DNA damage is not, even though RS and OIS activate the cellular DNA damage response pathway, highlighting the independence of senescence from cellular ageing. Consistent with this, we observed that telomerase-immortalised cells aged in culture without having been treated with any senescence inducers or DNA-damaging agents, re-affirming the independence of the process of ageing from telomeres and senescence. Collectively, our results reveal that cellular ageing is distinct from cellular senescence and independent of DNA damage response and telomere length.