ABSTRACT The detection of Earth-like planets with the radial-velocity (RV) method is currently limited by the presence of stellar activity signatures. On rotational time-scales, spots and plages (or faculae) are known to introduce different RV signals, but their corrections require better activity proxies. The best-known chromospheric activity proxies in the visible are the Ca ii H&K lines, but the physical quantities measured by their profiles need to be clarified. We first investigate resolved images of the Sun in order to better understand the spectrum of plages, spots, and the network using the Meudon spectroheliogram. We show that distinct line profiles are produced by plages, spots, and by the network component and we also derived the centre-to-limb variations of the three profiles. Some care is required to disentangle their contributions due to their similarities. By combining disc-integrated spectra from the ISS high-resolution spectrograph with SDO direct images of the Sun, we managed to extract a high-resolution emission spectrum of the different components, which tend to confirm the spectra extracted from the Meudon spectroheliogram datacubes. Similar results were obtained with the HARPS-N Sun-as-a-star spectra. We concluded using a three-component model that the temporal variation of the popular Sindex contains, on average for the 24th solar cycle: $70\pm 12{{\ \rm per\ cent}}$ of plage, $26\pm 12{{\ \rm per\ cent}}$ of network, and $4\pm 4 {{\ \rm per\ cent}}$ of spots. This preliminary investigation suggests that a detailed study of the Ca ii H&K profiles may provide rich information about the filling factor and distribution of different types of active regions.