This work explores the consequences that different energy poverty definitions and measures might have for the identification of the energy poor. Using the 2017 National Survey of Public Energy Perception applied to a sample of 3,500 households in Chile, we compare the respective identification outcomes of applying the ten percent rule index (TPRI) and our proposed Perception-based Multidimensional Energy Poverty Index (PMEPI) against the monetary poverty identification outcome. Based on the findings of this comparation, we propose a classification system of first- and second-order energy poverty measures depending on their degree of association with income poverty (as indicated by the distribution of the income poverty status of households). A first-order energy poverty measure exhibits a high association level with income poverty. By contrast, a second-order en-ergy poverty measure shows a low level of association. Coincidentally, our TPRI (first-order) and PMEPI (second- order) estimates each classify 15.5% of the population as energy poor. However, the adoption of any particular definition necessarily narrows the resulting set of energy-poor households in a way that is distinct from other definitions, meaning that the use of multiple definitions produces diverging energy poverty rankings across the territory. Moreover, the TPRI neglects supply-side constraints captured by the PMEPI. Consequently, when identifying and targeting the energy poor, first- and second-order definitions should not be used as substitutes but rather as complements. This fact needs to be considered in the energy policy debate on the implementation of energy poverty alleviation actions.