Our primary objective is to accurately identify and classify the variability of A-F stars in the southern continuous viewing zone of the TESS satellite. The brightness limit was set to 10 mag to ensure the utmost reliability of our results and allow for spectroscopic follow-up observations using small telescopes. We aim to compare our findings with existing catalogues of variable stars. The light curves from TESS and their Fourier transform were used to manually classify stars in our sample. Cross-matching with other catalogues was performed to identify contaminants and false positives We have identified 1171 variable stars (51% of the sample). Among these variable stars, 67% have clear classifications, which includes {delta} Sct and {gamma} Dor pulsating stars and their hybrids, rotationally variables, and eclipsing binaries. We have provided examples of the typical representatives of variable stars and discussed the ambiguous cases. We found 20 pairs of stars with the same frequencies and identified the correct source of the variations. Additionally, we found that the variations in 12 other stars are caused by the contamination with the light of faint nearby large-amplitude variable stars. To compare our sample with other variable star catalogues, we have defined two parameters reflecting the agreement in identification of variable stars and their classification. This comparison reveals intriguing disagreements in classification ranging from 52% to 100 %. However, if we assume that stars without specific types are only marked as variable, then the agreement is relatively good, ranging from 57% to 85% (disagreement 15-43%). We have demonstrated that the TESS classification is superior to the classification based on other photometric surveys. The classification of stellar variability is complex and requires careful consideration. Caution should be exercised when using catalogue classifications.