nlinfit uses optimization solvers under the hood, so it's not too surprising that you're getting the same answer.
nlinfit is part of Statistics Toolbox. As such, the function is designed to support typical workflows used by data analysts and provides some additional additional output parameters like R^2. You also have a variety of helper functions that you can use to compute confidence intervals, perform cross validation, and the like.
Optimization Toolbox is a general purpose tool which is both a strength and a weakness. On the plus side, Optimization Toolbox can be used to solve problems that nlinfit can't solve (or can't solve easily). Regression models that involve complex constraints are a classic example. On the down side, if you're trying to do basic data analysis tasks you'll probably need to write a lot more code by hand.