Rings and spiral arms are distinctive features of many galaxies, and their properties are closely related to the disk dynamics. They are often associated to stellar bars, but the details of this connection are far from clear... We study the pitch angles of spiral arms and the frequency and dimensions of inner and outer rings as a function of disk parameters and the amplitude of non-axisymmetries in the S$^4$G survey. The ring fraction increases with bar Fourier density amplitude: this can be interpreted as evidence for the role of bars in ring formation. The sizes of inner rings, normalised by the disk size, are positively correlated with bar strength: this can be linked to the radial displacement of the inner 4:1 ultra-harmonic resonance while the bar grows and the pattern speed decreases. The fraction of rings is larger in barred galaxies than in their non-barred counterparts, but still $\sim 1/3$ ($\sim 1/4$) of the galaxies hosting inner (outer) rings are not barred. The amplitudes of bars and spirals are correlated for all types of spirals. However, on average, the pitch angles of spiral arms are roughly the same for barred and non-barred galaxies: this questions the role of bars exciting spiral structure. We conclude that the present-day coupling of rings, spiral arms, and bars is not as robust as predicted by simulations. (read more)