Conduction, convection, and radiation are all forms of heat transfer, but they rely on different physical interactions to transfer heat. Conduction occurs when heated solid matter transfers heat. Convection relies on an intermediate substance to transfer heat. Radiation uses electromagnetic waves to transfer heat and doesn't require matter-to-matter contact.
Conductive materials have a low heat capacity, which means they experience large changes in temperature from small amounts of heat energy. If the reverse was true, the material would be a poor conductive but a good insulator. Convection occurs when a liquid or gaseous substance conducts heat, such as cooking with a convection air oven or boiling pot of water. The sun can transfer heat through the vacuum of space because it uses radiation, which does not involve any physical contact.
The study of the transfer of heat and the changes associated with it is called thermodynamics. Every substance has an internal energy based on the kinetic activity of its molecules. When this energy is transferred from one body or system, it is called heat. The transfer of heat can have a variety of effects, the most noticeable being phase transitions between solid, liquid and gas states. This is why ice melts into liquid water as it heats up.