Difference between residuals and idiosyncratic errors? I have a simple question. I want to know the difference between the residuals obtained from a model and idiosyncratic errors.

The biggest difference is that residuals is a term used in statistics and "idiosyncratic errors" isn't.
In statistics there is a distinction between error and residuals, where in the model
$$
y = f(x) + \varepsilon
$$
$\varepsilon$ is the error term, while
$$
r = y - \hat y
$$
where $\hat y$ is the fitted value, is the residual.
I did a quick online search and appears in publications be econometricians, like those slides

The basic panel data model is given by:
$$ y_{it} = \beta_0 + \beta_1 x_{1,it} + \beta_2 x_{2,it} + \dots +
 \beta_K x_{K,it} + a_i + u_{it}, \qquad (18) $$
with idiosyncratic errors $u_{it}$  [...]

where clearly they mean the error term. Same here where the author also has econometrics background, or discussed on /r/econometrics.
