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The OGLE database is revisited to investigate in more detail the propertiesof the Fourier parameters. Methodological improvements led us to identify aclear separation among High-Amplitude Delta Scuti (HADS), RRc and RRab stars.The bimodal distribution of the R21 parameter in HADS stars is explained as acontamination effect from RRc stars: there is evidence that all stars with0.20<P<0.25 d are RRc variables. The previously claimed existence of a subclassof unusual HADS is demonstrated to be a spurious result. Candidate overtonepulsators are found among HADS and RRc variables. The properties of the Fourierparameters are discussed as a function of the physical conditions in the starsinvolved. Among the field RRab stars we detected different light-curve groupsproducing distinct "tails" in the Fourier plots for P>0.55 d; evolutionaryphases or the combination of different physical conditions (not onlymetallicity) are suggested to explain this separation, observed also in thecluster RRab stars. The stellar parameters of RRc stars in a given globularcluster show different tendencies than those of RRc stars from differentclusters.Comment: 12 pages (in A&A style), 14 eps figures. Accepted for A&A Main  Journal. Table 3, 4 and 5 are also included as ascii files. The atlas of the  light curves and least-squares fits can be requested from the autho

Fourier decomposition and frequency analysis of the pulsating stars with $\vec{P< }$ 1 d in the OGLE database