What is the difference between $R^2$ and variance score in Scikit-learn?

I was reading about regression metrics in the python scikit-learn manual and even though each one of them has its own formula, I cannot tell intuitively what is the difference between $$R^2$$ and variance score and therefore when to use one or another to evaluate my models.

1. $$R^2 = 1- \frac{SSE}{TSS}$$
2. $$\text{explained variance score} = 1 – \mathrm{Var}[\hat{y} – y]\, /\, \mathrm{Var}[y]$$, where the $$\mathrm{Var}$$ is biased variance, i.e. $$\mathrm{Var}[\hat{y} – y] = \frac{1}{n}\sum(error – mean(error))^2$$. Compared with $$R^2$$, the only difference is from the mean(error). if mean(error)=0, then $$R^2$$ = explained variance score
3. Also note that in adjusted-$$R^2$$, unbiased variance estimation is used.