Linear continuous-time plants modeled, in general, with the aid of operator polynomials, are identified with the use of continuous-time regression models of two types, which result from 'differential' and 'integral' normalizations. Estimates of the parameters of these models are obtained via a 'finite-horizon' processing of the regression vector that contains consecutive multiple integrals of the plant input and output signals. Effective continuous-time identification is performed with the employment of the continuous-time least-squares and instrumental variable approaches. The continuous-time algorithms and the regression vectors are eventually transformed into the discrete-time domain by utilizing numerical integrating schemes. Ultimate discrete-time realizations are examined in a simulation study.