Specific heat of a solid or liquid is the amount of heat that raises the temperature of a unit mass of the solid through 1°C.
The Molar specific heat of a solid or liquid of a material is the heat that you provide to raise the temperature of one mole of solid or liquid through 1K or 1°C.
The volume of solid remains constant when heated through a small range of temperature. This is known as specific heat at a constant volume. It is denoted as CV.
The pressure of solid remains constant when heated through a small range of temperature. This is known as specific heat at constant pressure which can be denoted as CP.