A simple (two-variable) regression has three standard errors: one for each coefficient (slope, intercept) and one for the predicted Y (standard error of regression).

While the population regression function (PRF) is singular, sample regression functions (SRF) are plural. Each sample produces a different SRF. So, the coefficients exhibit dispersion (sampling distribution). The standard error is the measure of this dispersion: it is the standard deviation of the coefficient.

In this video, David from Bionic Turtle talks about the standard error in linear regression.