There are severeal word in Pali and Sanskrit who are often translated in to the English word mindfulness. These terms mean some different thing, as to why confusion may arise when you discuss mindfulness.
The word that is most often translated into mindfuless is Sati/Smriti, which means “to remember” (non-forgetfulness). It simply means that if we decide for ourselves to attach the mind at our present expecience, we will “remember” to hold it there, instead of letting it slip away.
Other words who also is commonly translated into mindfulness is Manisikara, who is the moment of ”pure perception” just before the mind starts to separate, judge and value. In the western interpretation of mindfulness (within psychology) an large emphasis is put on this.
Appamada/Apramada is about being thorough and calculated in your actions and not act överilat and unskillful. This is also an aspect of mindfulness.
Lastly we have Sampajanna/Samprajana which means to see clearly, to separate (skillful from unskillful).
The ability to stay with your experience , to see it clearly, to separate skillful and unskillful, and to act in a favourable are all aspects of “mindfulness”
May the force be with you