Latent heat is defined as a heat which is emitted or absorbed by a substance during the change of phase but without a temperature change. It is calculated by
L=Q/M

The unit for latent heat is J/Kg

Specific heat is defined as the change in temperature of substance but without change in phase like solid to liquid or vice versa. It is calculated by

q=m×s×∆t

The unit for specific heat is J/Kg. K