Which of the following are true based on this comparison?
A is not true - no such connection exists.
B is true (and given the same temperature indicating the phase transition it is in fact likely that K and L are the same matter).
C is true and can be explained as follows: if K and L have the same mass, they must have different specific heat capacities, defined as:

$$
c = \frac{\text{the amount of energy to be added to raise the temperature by 1°C}}{\text{mass}}
$$

This is a property that is unique for each matter - same as the melting and boiling point. It can be said to be a function of the matter. Note that the $T(t)$ graphs appear to start at the same temperature, but it takes longer to heat L than K to 85°C although the same heating is applied.