Photometric scaling relations are studied for S0 galaxies and compared with those obtained for spirals. New two-dimensional multi-component decompositions are presented for 122 early-type disc galaxies, using deep Ks-band images. Combining them with our previous decompositions, the final sample consists of 175 galaxies (Near-Infrared Survey of S0s, NIRS0S: 117 S0s + 22 S0/a and 36 Sa galaxies). As a comparison sample we use the Ohio State University Bright Spiral Galaxy Survey (OSUBSGS) of nearly 200 spirals, for which similar multi-component decompositions have previously been made by us. The improved statistics, deep images and the homogeneous decomposition method used allow us to re-evaluate the parameters of the bulges and discs. For spirals we largely confirm previous results, which are compared with those obtained for S0s. Our main results are as follows. (1) Important scaling relations are present, indicating that the formative processes of bulges and discs in S0s are coupled [e.g. M0K(disc) = 0.63 M0K(bulge) -9.3], as has been found previously for spirals [for OSUBSGS spirals M0K (disc) = 0.38 M0K(bulge) -15.5 the rms deviation from these relations is 0.5 mag for S0s and spirals]. (2) We obtain median reff/h0r ~ 0.20, 0.15 and 0.10 for S0, S0/a-Sa and Sab-Sc galaxies, respectively: these values are smaller than predicted by simulation models in which bulges are formed by galaxy mergers. (3) The properties of bulges of S0s are different from the elliptical galaxies, which are manifested in the versus reff relation, in the photometric plane (μ0, n, reff), and to some extent also in the Kormendy relation (< μ >eff versus reff). The bulges of S0s are similar to bulges of spirals with M0K(bulge) < -20 mag. Some S0s have small bulges, but their properties are not compatible with the idea that they could evolve to dwarfs by galaxy harassment. (4) The relative bulge flux (B/T) for S0s covers the full range found in the Hubble sequence, even with 13 per cent having B/T< 0.15, typical for late-type spirals. (5) The values and relations of the parameters of the discs [h0r, , μ0(0)] of the S0 galaxies in NIRS0S are similar to those obtained for spirals in the OSUBSGS. Overall, our results support the view that spiral galaxies with bulges brighter than -20 mag in the K band can evolve directly into S0s, due to stripping of gas followed by truncated star formation.