Is Mindfulness a poor translation for Sati?

Usually Sati is translated as Mindfulness, but according to the Wikipedia entry, Mindfulness is described as follows: >Mindfulness is the psychological process of bringing one's attention to experiences occurring in the present moment, which can be developed through the practice of meditation and other training. The term "mindfulness" is a translation of the Pali term sati, which is a significant element of Buddhist traditions. According to suttacentral's entry, Sati is defined as memory, recognition, consciousness, intentness of mind, wakefulness of mind etc. My question is then, is it a mistake to call Sati Mindfulness, since Minsfulness means awareness. Now Sati is always used with his close companion sampajañña, which in turn makes the attention always directed to moral attitudes etc., whereas "mainstream mindfulness" just observes inner and outer phenomena with an open, curious and beginners mind. Source: https://en.m.wikipedia.org/wiki/Mindfulness https://suttacentral.net/search?query=sati