There are different shades of interpretation of the terms Āstika-Nāstika.
Most of the answers on this forum relate to the interpretations that are propounded by some vested groups to denigrate other Indian faiths.
There is one question on this forum that could have been answered in the spirit of my question. However, it is married to another question, that reflects the general belief of the term Āstika-Nāstika and leaves no room to treat these terms divorced from the belief system. Hence, there is a need for a separate question.
However, the question that remains to be answered whether the terms Āstika-Nāstika can be explained without any connection to one particular faith or belief like Hinduism? Is there an etymological explanation for these terms?