Constant Year
Constant dollars is a term describing income after adjustment for inflation. Constant-dollar values represent an effort to remove the effects of price changes from statistical series reported in dollar terms. The result is a series as it would presumably exist if prices were the same throughout as they were in the base years.
Current Year
Nominal or Current dollars is a term describing income in the year in which a person, household, or family receives it. For example, the income someone received in 2015 unadjusted for inflation is in current dollars.