My 2018 statement says... "Your payment will be about $x,xxx a month at full retirement age". My FRA is in a few years.... if I claim at my FRA, I will get $x,xxx per month plus any COLA increases for 2019 and subsequent years between 2019 and my FRA.
On the second page, it also states "age 70, your payment will be about $y,yyy a month" if I wait until age 70 I will receive $y,yyy plus COLA increases for 2019 and subsequent years between 2019 and age 70.
In my case, I have been retired for a while so my post retirement years are all zeros and the SSA will assume that my future earnings will be zero.
So I guess it is more real than nominal since it will be increased for inflation between now when I start SS.