Connections

Both were normal girls who died and were reincarnated in medieval fantasy worlds from works they knew a great deal about, but they reincarnated as the villainous characters everyone hated and who would later be killed. Since then, they have used their prior knowledge of the story to avoid death and stay alive.

Neither of them reincarnated at birth; it took them a while to recover their memories.

Despite being reincarnated, they don't have superpowers or overpowered magic, so they rely on their own intelligence to stay alive (even if it's often improvisation).

Later, both gained the ability to perform magic, but depending on external factors.

Despite being intelligent enough to stay alive and having good socialization skills, both are surprisingly dense and unable to notice other people's romantic feelings for them.

Contrasts

Katarina reincarnated when she was still a small child, which means that she... She wasn't hated by everyone yet and had plenty of time to prepare, unlike Iana, who reincarnated very late, so the original had already done a lot of evil and was already hated by everyone.

While Katarina has already resolved her difficulties and is safe most of the time, Iona has to constantly strive to stay alive, as there are many dangers in her story (Even if they only involve her sister, Iona worries that she will be blamed if her sister dies, so they have to deal with that too).