Weighted Least Squares VS Weighted Nonlinear Regression in Matlab?

For weighted least squares, it can be used for all regression methods that invoke least squares, including nonlinear regression. In the description of Matlab, "http://www.mathworks.com/help/curvefit/least-squares-fitting.html", weighted least squares only adjusts the weighting when calculating the sum squares of residuals. However, for weighted nonlinear regression, "http://www.mathworks.com/help/stats/examples/weighted-nonlinear-regression.html", it's more like a data transform method. It will multiply a weighting function to the observed data and also the model that will be used for fitting.It seems that both these two methods could deal with the situation in which observed data are with nonconstant error variance. So, what's the difference between them? Thank you.