What is the difference between the law and def of congruence? I dont understand when to use which one, does it matter?
Not sure what you mean by "law" of congruence. Two plane geometric figures are said to be congruent if they have the same size and shape.
Angles are congruent if their measures are equal.
Segments are congruent if their lengths are the same.
Polygons are congruent if their corresponding sides and angles are congruent.
The difference between "congruent" and "equal" deals with whether it's a geometric figure or a value of measurement.
For instance, $\displaystyle \overline{AB}\cong\overline{CD}$ only if $\displaystyle AB=CD$. $\displaystyle AB$ and $\displaystyle CD$ represent real numbers, whereas $\displaystyle \overline{AB}$ and $\displaystyle \overline{CD}$ represent shapes.