Example 2 Find the range of $y=\sqrt{x^{2}-2 x+5}-$ $\sqrt{x^{2}-6 x+13}$.
Solution: The original expression is transformed into
$$
y=\sqrt{(x-1)^{2}+2^{2}}-\sqrt{(x-3)^{2}+2^{2}},
$$

where the fixed points are $A(1,2), B(3,2)$.
Clearly, the line $AB \parallel x$-axis, and $|AB|=|3-1|=2$,
$\therefore$ the range is $(-2,2)$.
$2 y=\sqrt{\left(x-x_{1}\right)^{2}+y_{1}^{2}}+\sqrt{\left(x-x_{2}\right)^{2}+y_{2}^{2}}$