Using simulated galaxies in their cosmological context, we analyse how the flaring of mono-age populations (MAPs) influences the flaring and the age structure of geometrically defined thick discs. We also explore under which circumstances the geometric thin and thick discs are meaningfully distinct components, or are part of a single continuous structure as in the Milky Way. We find that flat thick discs are created when MAPs barely flare or have low surface density at the radius where they start flaring. When looking at the vertical distribution of MAPs, these galaxies show a continuous thin/thick structure. They also have radial age gradients and tend to have quiescent merger histories. Those characteristics are consistent with what is observed in the Milky Way. Flared thick discs, on the other hand, are created when the MAPs that flare have a high surface density at the radius where they start flaring. The thick discs’ scale heights can either be dominated by multiple MAPs or just a few, depending on the mass and scale height distribution of the MAPs. In a large fraction of these galaxies, thin and thick discs are clearly distinct structures. Finally, flared thick discs have diverse radial age gradients and merger histories, with galaxies that are more massive or that have undergone massive mergers showing flatter age radial gradients in their thick disc.