How to interpret the difference between natural level and steady state in Macroeconomic theory I am reading Monetary policy, inflation, and the business cycle: an introduction to the new Keynesian framework and its applications by Gali.

In this question I am going to use the output $Y_t$ as an example. I am going to use the notation from Gali.


$y$ is notation for the steady state. 
$y_t^n$ is notation for the the natural level of output.
$\tilde{y}_t = y_t-y_t^n$ is the output gap: deviation from the natural level.
$\hat{y}_t = y_t-y$ is the deviation from steady state.


My question is: Intuitively speaking, what is the difference between steady state level and natural level? 

Note: $y_t = \log Y_t$
Natural level of output is equivalent to full employment output. This does not mean full employment of all resources, there is always a natural level of unemployment even in full employment output level. 

Neoclassical economics: Steady state output is achieved when capital-labour ratio is stable or constant. In steady state, economy is not growing and also not in recession, all variales grow at the same rate i.e. birth rates equal death rates, capital accumulation rates equal depreciation rates, etc.