# What exactly does "wald test" mean?

I am reading possibly conflicting statements in different sources.

Sometimes I think I understand that the word "Wald test" refers to

• any kind of test of whether the value of a parameter (whether in a linear model or not) is significantly removed from a null hypothesis. i.e. the Wald test outputs one of $\{\text {Reject},\text{Not-Reject} \}$ given a rejection threshold $\alpha$ (usually 0.05 or 0.01), of the likelihood that a test statistic $S$ farther away from $S_0$ would be obtained if the null hypothesis is true,

• The above, but specifically to coefficent parameters in a linear regression model.

• The above, but specifically taking the population variance $\sigma^2$ as given. (i.e. a $t$ test is not a Wald test).

Which of these is it, or is it something else?