Two alternative models for the origin of the broad and intermediate-width lines in the spectrum of the peculiar supernova SN 1988Z are proposed. Both suggest that the optical emission is a result of the dynamical interaction of the ejecta with a two-component wind; the broad lines are identified with emission from shocked supernova material expanding in a relatively rarefied wind, while the intermediate-width lines originate from a shocked dense wind component. The latter may be associated either with dense wind clumps or with a dense equatorial wind. The clumpy-wind model is more attractive since it requires a lower mass loss. The optical emission of SN 1986J at t = 4 yr, which in many respects is similar to the intermediate component of SN 1988Z, is probably also produced by shocked dense clumps in the circumstellar wind component. Dynamical properties and the luminosity of the broad lines imply that the mass of the SN 1988Z ejecta is unexpectedly low, M < 1 M_sun_, suggesting that SN 1988Z may have originated from a star with a main-sequence mass of about 8-10 M_sun_.