Yes, we suspect the same, and finding the birth parents would eliminate all doubts. Because of the 3 Lacey grandchildren in the census, Catherine McDonald is likely my Great great grandmother, Catherine Lacey. Her husband James passed in 1888 and her trail goes cold after the1892 (?) NY census. One of her children, Peter, passed in 1895, and we have a marriage record of a Catherine Lacey, daughter of Peter. So there seems to be a high likelihood that the 1900 Kate A. Is the same person.