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The two planetary systems TOI-942 and TOI-421 share many similarcharacteristics, apart from their ages (50~Myr and 9~Gyr). Each of the starshosts two sub-Neptune-like planets at similar orbits and in similar massranges. In this paper, we aim to investigate whether the similarity of the hoststars and the configuration of the planetary systems can be taken as proof thatthe two systems were formed and evolved in a similar way. In paper I of thisseries, we performed a comparative study of these two systems using 3D modelingof atmospheric escape and its interaction with the stellar wind, for the fourplanets. We demonstrated that though the strong wind of the young star has acrucial effect on observable signatures, its effect on the atmospheric massloss is minor in the evolutionary context. Here, we use atmosphere evolutionmodels to track the evolution of planets in the younger system TOI-942 and alsoto constrain the past of the TOI-421 system. We demonstrate that despite allthe similarities, the two planetary systems are on two very differentevolutionary pathways. The inner planet in the younger system, TOI-942, willlikely lose all of its atmosphere and become a super-Earth-like planet, whilethe outer planet will become a typical sub-Neptune. Concerning the oldersystem, TOI-421, our evolution modeling suggests that they must have startedtheir evolution with very substantial envelopes, which can be a hint offormation beyond the snow line.

Atmospheric mass loss and stellar wind effects in young and old systems II: Is TOI-942 the past of TOI-421 system?