This paper introduces a quadrature-free, non-intrusive approach to balanced truncation for both continuous-time and discrete-time systems. The method non-intrusively constructs reduced-order models using available transfer function samples from the right half of the $s$-plane. It is highlighted that the proposed data-driven balanced truncation and existing quadrature-based balanced truncation algorithms share a common feature: both compress their respective data quadruplets to derive reduced-order models. Additionally, it is demonstrated that by using different compression strategies, these quadruplets can be utilized to develop three non-intrusive formulations of the IRKA for both continuous-time and discrete-time systems. These formulations non-intrusively generate reduced models using transfer function samples from the $jω$-axis or the right half of the $s$-plane, or impulse response samples. Notably, these IRKA formulations eliminate the necessity of computing new transfer function samples as IRKA iteratively updates the interpolation points. The efficacy of the proposed algorithms is validated through numerical examples, which show that the proposed non-intrusive approaches perform comparably to their intrusive counterparts.