(1) Background: Many vaccines require higher, additional doses or adjuvants to provide adequate protection for people living with HIV (PLWH). Despite their potential risk of severe coronavirus disease 2019, immunological data remain sparse, and a clear consensus for the best booster strategy is lacking. (2) Methods: Using the data obtained from our previous study assessing prospective T-cell and humoral immune responses before and after administration of a third dose of SARS-CoV-2 vaccine, we assessed the correlations between immune parameters reflecting humoral and cellular immune responses. We further aimed at identifying distinct clusters of patients with similar patterns of immune response evolution to determine how these relate to demographic and clinical factors. (3) Results: Among 80 PLWH and 51 healthcare workers (HCWs) enrolled in the study, cluster analysis identified four distinct patterns of evolution characterised by specific immune patterns and clinical factors. We observed that immune responses appeared to be less robust in cluster A, whose individuals were mostly PLWH who had never been infected with SARS-CoV-2. Cluster C, whose individuals showed a particularly drastic increase in markers of humoral immune response following the third dose of vaccine, was mainly composed of female participants who experienced SARS-CoV-2. Regarding the correlation study, although we observed a strong positive correlation between markers mirroring humoral immune response, markers of T-cell response following vaccination correlated only in a lesser extent with markers of humoral immunity. This suggests that neutralising antibody titers alone are not always a reliable reflection of the magnitude of the whole immune response. (4) Conclusions: Our findings show heterogeneity in immune responses among SARS-CoV-2 vaccinated PLWH. Specific subgroups could therefore benefit from distinct immunization strategies. Prior or breakthrough natural infection enhances the activity of vaccines and must be taken into account for informing global vaccine strategies among PLWH, even those with a viro-immunologically controlled infection.