Modern power systems are experiencing the challenge of high uncertainty with the increasing penetration of renewable energy resources and the electrification of heating systems. In this paradigm shift, understanding electricity users' demand is of utmost value to retailers, aggregators, and policymakers. However, behind-the-meter (BTM) equipment and appliances at the household level are unknown to the other stakeholders mainly due to privacy concerns and tight regulations. In this paper, we seek to identify residential consumers based on their BTM equipment, mainly rooftop photovoltaic (PV) systems and electric heating, using imported/purchased energy data from utility meters. To solve this problem with an interpretable, fast, secure, and maintainable solution, we propose an integrated method called Interpretable Refined Motifs And binary Classification (IRMAC). The proposed method comprises a novel shape-based pattern extraction technique, called Refined Motif (RM) discovery, and a single-neuron classifier. The first part extracts a sub-pattern from the long time series considering the frequency of occurrences, average dissimilarity, and time dynamics while emphasising specific times with annotated distances. The second part identifies users' types with linear complexity while preserving the transparency of the algorithms. With the real data from Australia and Denmark, the proposed method is tested and verified in identifying PV owners and electrical heating system users.