In this paper, we consider the transmission of confidential information over an α-μ and a κ-μ fading channel in the presence of an eavesdropper who experiences κ-μ and α-μ fading, respectively. In particular, we derive novel analytical expressions for the probability of strictly positive secrecy capacity (SPSC) and a lower bound on secrecy outage probability (SOPL) for independent and non-identically distributed (i.n.i.d.) channel coefficients. These results have been validated through simulations and reduction to known special cases. These new, very general formulations, are important as they bring together previously non-unified secrecy capacity and secrecy outage probabilities (SOP) such as those involving α-μ, Nakagami-m, Rayleigh, OneSided Gaussian, Weibull, Negative Exponential with κ-μ and Rice. Additionally, due to the duality of analysis of secrecy capacity and co-channel interference (CCI), the results presented here will also have immediate applicability in the analysis of outage probability in wireless systems affected by CCI and background noise for the aforementioned fading scenarios.