We present the first combined study of correlators and spectral properties of charmonium and open charm mesons at finite temperature using a fully relativistic lattice QCD approach. The QCD medium is captured by second generation anisotropic 243×Nτ lattices from the FASTSUM Collaboration, including 2+1 flavors of clover discretized quarks with mπ≈380  MeV. Two Bayesian methods are deployed to reconstruct the spectral functions, the recent Bayesian reconstruction (BR) method as well as the maximum entropy method with Fourier basis. We take particular care to disentangle genuine in-medium effects from method artifacts with the help of the reconstructed correlator. Consistent with the direct inspection of correlators, we observe no significant in-medium modification for J/Ψ and ηc around the crossover, while the χc states on the other hand show clear changes around the transition. At the highest temperature, T=352  MeV, J/Ψ and ηc also exhibit discernible changes compared to the vacuum. For D mesons around Tc, no significant modifications are observed, but we find clear indications that no bound state survives at the highest temperature of T=352  MeV. Above Tc we discover a significant difference between D and D∗ mesons, the latter being much more strongly affected by the medium.