Inner bars are frequent structures in the local Universe and thought to substantially influence the nuclear regions of disc galaxies. In this study we explore the structure and dynamics of inner bars by deriving maps and radial profiles of their mean stellar population content and comparing them to previous findings in the context of main bars. To this end, we exploit observations obtained with the integral-field spectrograph MUSE of three double-barred galaxies in the TIMER sample. The results indicate that inner bars can be distinguished based on their stellar population properties alone. More precisely, inner bars show elevated metallicities and depleted [$\alpha$/Fe] abundances. Although they exhibit slightly younger stellar ages compared to the nuclear disc, the typical age differences are small, except at their outer ends. These ends of the inner bars are clearly younger compared to their inner parts, an effect known from main bars as orbital age separation. In particular, the youngest stars (i.e. those with the lowest radial velocity dispersion) seem to occupy the most elongated orbits along the (inner) bar major axis. We speculate that these distinct ends of bars could be connected to the morphological feature of ansae. Radial profiles of metallicity and [$\alpha$/Fe] enhancements are flat along the inner bar major axis, but show significantly steeper slopes along the minor axis. This radial mixing in the inner bar is also known from main bars and indicates that inner bars significantly affect the radial distribution of stars. In summary, based on maps and radial profiles of the mean stellar population content and in line with previous TIMER results, inner bars appear to be scaled down versions of the main bars seen in galaxies. This suggests the picture of a "galaxy within a galaxy", with inner bars in nuclear discs being dynamically equivalent to main bars in main galaxy discs.