No they are quite different plants, although they have similar maori names. In botany the scientific names are the correct ones to use to name a plant.
For instance in New Zealand there are about 9 DIFFERENT species all called rata, they all have the Generic name of Metrosideros (like their surname) but different specific (first) names; like Metrosideros robusta -northern rata, Metrosideros fulgens - orange flowered rata, Metrosideros diffusa - one of the white-flowered rata etc.
These two puka species are not closely related because they don't share the same Generic name (surname).