lsqcurvefit for exponential regression - objective function

I read online about fitting an exponential curve to my data via least squares and I have understood it. http://mathworld.wolfram.com/LeastSquaresFittingExponential.html In matlab however, I am not sure what algorithm is being used if I pass in my arguments below. Can someone explain to me the theory behind matlab's least squares fit ?

1. Rather than compute the sum of squares, lsqcurvefit requires the user-defined function to compute the vector-valued function. What does this mean and how is this different from computing least squares ?

2. What is the default algorithm being used in my code below ? Least squares ? Or the trust region algorithm (I have no read what that is about)

3. What is the difference between x and xdata ? https://www.mathworks.com/help/optim/ug/lsqcurvefit.html#buuu2mv-1

F = @(p,xdata) p(1)*exp(p(2)*(xdata+p(3)));
x0 = [5 0 -10];
[p,resnorm] = lsqcurvefit(F,x0,xdata,ydata);