I have one week old cilantro and chilli seedlings growing in adjacent pots. They look the same. Are they supposed to look the same?
Yes, cilantro (AKA coriander) seedlings look very similar to pepper seedlings before they grow their second leaves (or their first true leaves). Eggplant seedlings look about the same as peppers, too. Tomatoes look similar, but are often a little redder in the stem and furrier everywhere. In the pictures here, the peppers have sharper leaf points than the cilantro. Peppers usually have leaf-points about like that, but I imagine there may be exceptions, since there are lots of varieties of peppers (and species, too). There are even furry pepper plants (e.g. rocoto, goats weed and black cobra).
The why has to do with genetics and if they look similar it means they share similarities in ancestry for that early stage of life.
Additional information: https://en.wikipedia.org/wiki/Plant_genetics