Standard error of estimator is the same as standard error of difference of estimator and parameter?

I was reading through some notes deriving the different variances for confidence and prediction in OLS. Before dwelving into it though, the notes say that the standard error of $b_1$ (estimator for the slope coefficient in SLR) is the same as the standard error of $b_1 - \beta_1$ where $\beta_1$ is the slope parameter...In other words $\text{Stderr}(b_1) = \text{Stderr}(b_1 - \beta_1)$. I'm not sure I can make sense of this unless $\beta_1$ is a constant?

flag	asked Jul 22 2011 at 1:53 Palace 1

Of course $\beta_{1}$ is a constant- that's fundamental to classical linear regression. The assumption is that there's a "true" but unknown model $y=\beta_{0}+\beta_{1}x$, and you're trying to estimate the parameters $\beta$ from noisy $y$ observations taken at precisely known $x$ values. – Brian Borchers Jul 22 2011 at 2:47

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