This paper presents a detailed analysis of post-Newtonian (PN) expansions of the next-to-leading order (NLO) post-Minkowskian (PM) gravitational waveforms derived from the scattering of two massive scalar objects and the emission of one graviton. The authors calculate the PN limit of the tree-level and one-loop amplitudes, obtaining an expansion up to the third subleading PN order. They provide explicit expressions for the multipole decomposition of these results in the center-of-mass frame and compare them with the results obtained from the classical Multipolar post-Minkowskian (MPM) method. The authors find perfect agreement between the two approaches once the BMS supertranslation frame is properly adjusted and the infrared divergences due to rescattering are suitably subtracted in dimensional regularization. The paper discusses the infrared divergences that arise in the Compton cuts due to tail or rescattering effects, which can be exponentiated into a (divergent) phase factor. The authors show that these divergences can be reabsorbed into a shift or "renormalization" of the observer's retarded time. They also discuss the PN expansion of the amplitude-based waveform, focusing on the real and imaginary parts of the kernel. The authors find that the results from the amplitude-based approach agree with the MPM results when the BMS supertranslation frame is properly adjusted and the infrared divergences are subtracted. The paper also discusses the multipolar post-Minkowskian (MPM) method, which is based on the PN solution of the Einstein equations in the near zone, followed by a matching with the multipole expansion of the gravitational field in the exterior zone. The authors show that the MPM method can be used to calculate the radiative multipoles of the gravitational waveform. They compare the results from the amplitude-based approach with those from the MPM method and find perfect agreement once the BMS supertranslation frame is properly adjusted and the infrared divergences are subtracted. The paper concludes that the amplitude-based approach can be applied beyond the soft-regime, ensuring agreement between amplitude-based and MPM results for generic frequencies. The authors also highlight the importance of BMS supertranslations in comparing amplitude-based results with those from the MPM method. The results show that the amplitude-based approach can be used to calculate the gravitational waveform with high precision, providing a valuable tool for gravitational wave astronomy.This paper presents a detailed analysis of post-Newtonian (PN) expansions of the next-to-leading order (NLO) post-Minkowskian (PM) gravitational waveforms derived from the scattering of two massive scalar objects and the emission of one graviton. The authors calculate the PN limit of the tree-level and one-loop amplitudes, obtaining an expansion up to the third subleading PN order. They provide explicit expressions for the multipole decomposition of these results in the center-of-mass frame and compare them with the results obtained from the classical Multipolar post-Minkowskian (MPM) method. The authors find perfect agreement between the two approaches once the BMS supertranslation frame is properly adjusted and the infrared divergences due to rescattering are suitably subtracted in dimensional regularization. The paper discusses the infrared divergences that arise in the Compton cuts due to tail or rescattering effects, which can be exponentiated into a (divergent) phase factor. The authors show that these divergences can be reabsorbed into a shift or "renormalization" of the observer's retarded time. They also discuss the PN expansion of the amplitude-based waveform, focusing on the real and imaginary parts of the kernel. The authors find that the results from the amplitude-based approach agree with the MPM results when the BMS supertranslation frame is properly adjusted and the infrared divergences are subtracted. The paper also discusses the multipolar post-Minkowskian (MPM) method, which is based on the PN solution of the Einstein equations in the near zone, followed by a matching with the multipole expansion of the gravitational field in the exterior zone. The authors show that the MPM method can be used to calculate the radiative multipoles of the gravitational waveform. They compare the results from the amplitude-based approach with those from the MPM method and find perfect agreement once the BMS supertranslation frame is properly adjusted and the infrared divergences are subtracted. The paper concludes that the amplitude-based approach can be applied beyond the soft-regime, ensuring agreement between amplitude-based and MPM results for generic frequencies. The authors also highlight the importance of BMS supertranslations in comparing amplitude-based results with those from the MPM method. The results show that the amplitude-based approach can be used to calculate the gravitational waveform with high precision, providing a valuable tool for gravitational wave astronomy.