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 lattices from the FASTSUM Collaboration, including flavors of clover discretized quarks with . 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 and around the crossover, while the states on the other hand show clear changes around the transition. At the highest temperature, , and also exhibit discernible changes compared to the vacuum. For mesons around , no significant modifications are observed, but we find clear indications that no bound state survives at the highest temperature of . Above we discover a significant difference between and mesons, the latter being much more strongly affected by the medium.