Yes. Sati is another misinterpreted Pali word.
Sati means keeping the mind on a particular arammana. That can be good or bad.
– Miccha sati is keeping the mind on a defiled arammana, say, stealing something, sexual misconduct, etc.
– Samma sati is keeping the mind on moral thought objects. That can have a wide range from, say, thinking about giving to focusing on a deep Dhamma concept.
Samadhi is a related word that also has been misinterpreted.
– Miccha sati leads to miccha samadhi. Thus, one ‘s mind will focus on a misdeed or a wrong view.
– Samma sati leads to samma samadhi. Here, one’s mind will be focused on a moral deed or a concept.
Sybe wrote: “Thinking about this the thought of conscience came to mind.
A conscientious person is also concerned with keeping the mind clean, undefiled with immoral thoughts, speech and actions. He/she has a strong sense of moral shame and dread (two treasures).”
That is right. What you describe is samma sati.