Financial year (FY) and assessment year in income tax laws are different.
From an income tax perspective, FY is the year in which income is earned. AY is the year following the financial year in which the taxpayer has to evaluate the previous year's income and pay taxes on it.
For instance, if the financial year runs from April 1, 2018, to March 31, 2019, then it is known as FY2018-19. The assessment year for the money earned during this period would begin after the financial year ends – that is from April 1, 2019 to March 31, 2020. Hence, the assessment year would be AY 2019-20.