Simply put, FY stands for Financial Year where income is earned by an individual or any other entity. It is the period from April 1 of a given year to March 31 of the succeeding year. AY stands for Assessment Year and it is the period of 12 months immediately succeeding after the closing of a given FY. It is the year in which the income earned by an individual or any other entity from the corresponding financial year is computed and reported to the income tax authorities.
The AY succeeds the FY and the FY precedes the AY by the same logic. Assuming the case of FY 2019-20 would mean that it starts from April 1, 2019 to March 31, 2020. For the same FY, the AY will be from April 1, 2020 to March 31, 2021. Both the years begin and end on the same date and for tax computation purposes; FY 2019-20 and AY 2020-21 are treated as the same.