The powerful magnetic storm (MS) in May 2024, which occurred almost 20 years after a series of similar events in the early 21st century, has attracted great interest and a number of publications. The objective of the study in this paper was to examine what the powerful magnetic storm revealed in answering the questions: (1) are the ionosonde measurements correct, (2) are the foF2 and TEC parameters interchangeable, (3) does the empirical IRI-Plas model correspond to the experimental data, (4) are there any features in the behavior of the ionospheric parameters in the two hemispheres? The results of using the data from 10 ionosondes and 33 GPS receiver points along the 15° E meridian showed: (1) at many stations there were no measurements from the beginning of the main phase of the MS until the middle of the recovery phase; at those stations where measurements were available, low foF2 and hmF2 values were observed (foF2~2 MHz, hmF2 < 200 km). (2) A very high correlation was observed between the foF2 and TEC parameters both for the entire sufficiently disturbed month in general (0.84–0.9) and during the disturbance period (0.84–0.93 except for the Athens station with 0.715). (3) For the foF2 and TEC parameters, the most accurate was the IRI-Plas model adapted to the experimental TEC values, with average values of MAE(foF2) = 0.77 MHz, RMSE(foF2) = 1.01 km, MAPE(foF2) = 13.88%, MAE(TEC) = 1.42 TECU, RMSE(TEC) = 1.85 TECU, MAPE = 6.95%. For hmF2, the closest to the experimental data were the medians with average values of MAE = 30.13 km, RMSE = 49.27 km, MAPE = 15.1%. (4) A large asymmetry in the response of the ionosphere of the two hemispheres to the MS was observed: in the southern hemisphere, an extremely large positive disturbance was observed in the period close to the minimum of Dst (δТЕС up to ~500%), while in the northern hemisphere, from the very beginning of the MS, there was a negative main phase, which turned into a two-stage negative recovery phase.