Suppose I have a mathematical model $y=mx$ and I have data for $x$ and $y$ and I want to fit the mathematical model on the data and determine the value of slope. I also have uncertainties of $x$ and $y$. The uncertainty in the slope of the fit can be calculated from the data and the fit. But I can also quantify the uncertainty in the slope by transferring $x$ and $y$ uncertainties for individual points to uncertainty $m$ for individual values.
My questions is: Whats the difference?
My guess is that the total uncertainty in $m$ is the combination of both of these uncertainties. Because the equation to calculate the uncertainty of slope does not include the uncertainty of $x$ and $y$.