# Difference between long run coefficient and non stochastic steady state coefficient ARDL model

I am a little bit confused on the definition of long run equilibrium coefficient. Suppose I have an ARDL model as:

$$y_t = \rho_1 y_{t-1} + \rho_2 y_{t-2} + \beta_1x_{t-1} + \beta_2x_{t-2}$$

The steady state non stochastic solution is:

$$y=\frac{ \beta_1 + \beta_2 }{1- \rho_1 -\rho_2}x$$

What is the definition of long run equilibrium coefficient for $$x$$ here? Is it defined as the coefficient of the steady state non stochastic solution $$\frac{ \beta_1 + \beta_2 }{1- \rho_1 -\rho_2}$$? What is the difference between the two concepts?

$$\frac{ \beta_1 + \beta_2 }{1- \rho_1 -\rho_2}$$