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We perform plasma diagnostics, including that of the non-Maxwellian $κ$-distributions, in several structures observed in the solar corona by the Extreme-Ultraviolet Imaging Spectrometer (EIS) onboard the Hinode spacecraft. To prevent uncertainties due to the in-flight calibration of EIS, we selected spectral atlases observed shortly after the launch of the mission. One spectral atlas contains an observation of an active region, while the other is an off-limb quiet Sun region. To minimize the uncertainties of the diagnostics, we rely only on strong lines and we average the signal over a spatial area within selected structures. Multiple plasma parameters are diagnosed, such as the electron density, differential emission measure, and the non-Maxwellian parameter $κ$. To do that, we use a simple, well-converging iterative scheme based on refining the initial density estimates via the DEM and $κ$. We find that while the quiet Sun spectra are consistent with a Maxwellian distribution, the coronal loops and moss observed within active region are strongly non-Maxwellian with $κ$ $\lessapprox$ 3. These results were checked by calculating synthetic ratios using DEMs obtained as a function of $κ$. Ratios predicted using the DEMs assuming $κ$-distributions converged to the ratios observed in the quiet Sun and coronal loops. To our knowledge, this work presents a strong evidence of a presence of different electron distributions between two physically distinct parts of the solar corona.