It is shown that the likeness of the periodogram and the LS-spectrum (both estimators of the power spectrum are widely used in the spectral analysis of time series), depends on the properties of the spectral window W(omega ) corresponding to the distribution of time points. The main results are: a) all the estimators evaluated at frequency omega are identical if W(2omega )=0; b) the Schuster periodogram differs from the LS-spectra at the frequencies omega =hat ω_k/2, where hat ω_k are the frequencies at which the spectral window has large side peaks due to irregular distribution of time points. Two examples for situations typical in astronomy illustrate these conclusions.