Context. About 20% of low-redshift galaxies are late-type spirals with a small or no bulge component. Although they are the simplest disk galaxies in terms of structure and dynamics, the role of the different physical processes driving their formation and evolution is not yet fully understood. Aims: We investigated whether small bulges of late-type spirals follow the same scaling relations traced by ellipticals and large bulges and if small bulges are disk-like or classical bulges. Methods: We derived the photometric and kinematic properties of nine nearby late-type spirals. To this aim, we analyzed the surface-brightness distribution from the i-band images of the Sloan Digital Sky Survey and obtained the structural parameters of the galaxies from a two-dimensional photometric decomposition. We found a bulge component in seven galaxies of the sample, while the remaining two resulted in pure disk galaxies. We measured the line-of-sight stellar velocity distribution within the bulge effective radius from the long-slit spectra taken with high spectral resolution at the Telescopio Nazionale Galileo. We used the photometric and kinematic properties of the sample bulges to study their location in the fundamental plane, Kormendy, and Faber-Jackson relations defined for ellipticals and large bulges. Results: We found that our bulges satisfy some of the photometric and kinematic prescriptions for being considered disk-like bulges, such as small sizes and masses with nearly exponential light profiles, small bulge-to-total luminosity ratios, low stellar velocity dispersions, and ongoing star formation. However, each of these bulges follows the same scaling relations of ellipticals, massive bulges, and compact early-type galaxies so they cannot be classified as disk-like systems. Conclusions: We find a single population of galaxy spheroids that follow the same scaling relations, where the mass seems to lead to a smooth transition in the photometric and kinematic properties from less massive bulges to more massive bulges and ellipticals.