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When two solids absorb the same amount of heat but reach different final temperatures, the key factor that accounts for this difference is specific heat. Specific heat is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius.

If the materials have different specific heat capacities, they will respond differently to the same amount of heat energy. For instance, a substance with a higher specific heat will experience a smaller increase in temperature compared to a substance with a lower specific heat when the same amount of heat is added. This means that even if both solids absorb the same quantity of heat, the one with the lower specific heat will achieve a higher final temperature.

The other options, such as heat of fusion and heat of vaporization, pertain to phase changes of matter (solid to liquid, or liquid to gas) and are not relevant to the situation mentioned, where there is no phase change occurring. Conductive heat is not a term that directly applies in this context regarding temperature change of solids without considering the medium through which heat is being transferred.

Thus, the definitive difference in final temperatures, despite equal heat absorption, emerges from the variation in specific heat capacities of the substances involved.