Purpose: To evaluate and compare corneal hysteresis (CH), corneal resistance factor (CRF), and central corneal thickness (CCT), measurements were taken between a healthy population (controls), patients diagnosed with glaucoma (DG), and glaucoma suspect patients due to ocular hypertension (OHT), family history of glaucoma (FHG), or glaucoma-like optic discs (GLD). Additionally, Goldmann-correlated intraocular pressure (IOPg) and corneal-compensated IOP (IOPcc) were compared between the different groups of patients. Methods: In this prospective analytical-observational study, a total of 1065 patients (one eye of each) were recruited to undergo Ocular Response Analyzer (ORA) testing, ultrasound pachymetry, and clinical examination. Corneal biomechanical parameters (CH, CRF), CCT, IOPg, and IOPcc were measured in the control group (n = 574) and the other groups: DG (n = 147), FHG (n = 78), GLD (n = 90), and OHT (n = 176). We performed a variance analysis (ANOVA) for all the dependent variables according to the different diagnostic categories with multiple comparisons to identify the differences between the diagnostic categories, deeming p < 0.05 as statistically significant. Results: The mean CH in the DG group (9.69 mmHg) was significantly lower compared to controls (10.75 mmHg; mean difference 1.05, p < 0.001), FHG (10.70 mmHg; mean difference 1.00, p < 0.05), GLD (10.63 mmHg; mean difference 0.93, p < 0.05) and OHT (10.54 mmHg; mean difference 0.84, p < 0.05). No glaucoma suspects (FHG, GLD, OHT groups) presented significant differences between themselves and the control group (p = 1.00). No statistically significant differences were found in the mean CRF between DG (11.18 mmHg) and the control group (10.75 mmHg; mean difference 0.42, p = 0.40). The FHG and OHT groups showed significantly higher mean CRF values (12.32 and 12.41 mmHg, respectively) than the DG group (11.18 mmHg), with mean differences of 1.13 (p < 0.05) and 1.22 (p < 0.001), respectively. No statistically significant differences were found in CCT in the analysis between DG (562 μ) and the other groups (control = 556 μ, FHG = 576 μ, GLD = 569 μ, OHT = 570 μ). The means of IOPg and IOPcc values were higher in the DG patient and suspect groups than in the control group, with statistically significant differences in all groups (p < 0.001). Conclusion: This study presents corneal biomechanical values (CH, CRF), CCT, IOPg, and IOPcc for diagnosed glaucoma patients, three suspected glaucoma groups, and a healthy population, using the ORA. Mean CH values were markedly lower in the DG group (diagnosed with glaucoma damage) compared to the other groups. No significant difference was found in CCT between the DG and control groups. Unexpectedly, CRF showed higher values in all groups than in the control group, but the difference was only statistically significant in the suspect groups (FHG, GLD, and OHT), not in the DG group.