Smriti is correct Sanskrit of Pali 'Sati'. The 'Sati' you are talking about is a different thing. This 'Sati' is related to mindfulness.
It is a Hindu religious practice of taking the life of a Hindu widow after her Husband dies( https://en.wikipedia.org/wiki/Sati_(practice) ). The central idea is to prevent remarriage with other caste men and preserve the purity of caste system.