Conduction can refer to either:
The word conductor usually means a material with high electrical conductivity (low resistivity). However, most electric conductors (usually metals), are good thermal conductors as well. For example, copper is both an excellent thermal conductor and electrical conductor.
The reverse is usually but not always true; for example, diamonds are excellent thermal conductors (even better than copper) but usually electrical insulators. Although at very low temperatures a research group found  showing that diamonds can become superconductors below 4 K (superconductivity is specifically a description of electrical conduction, not thermal conduction).