The wald is for logistic regression. it's a test of significance for the individual variables and the whole model based on the chi squared distribution. ...and I don't know about the chi square in linear. I've never used a chi squared in linear reg. Sorry. You get half an answer.
I'm also working on a nonlinear regression, so the wald-chi square is the same as chi square but it is wald only because it is used for testing a nonlinear regression. Am I right?
Actually I don't know what does the value of wald chi-square mean for each parameter. Should this value be high or low?