This paper investigates the statistical properties of the Tully-Fisher (TF) relations for a volume-limited complete sample of spiral galaxies in the nearby Ursa Major Cluster. The merits of B, R, I, and K' surface photometry and the availability of detailed kinematic information from H I synthesis imaging have been exploited. In addition to the corrected H I global profile widths WiR,I, the available H I rotation curves allow direct measurements of the observed maximum rotational velocities Vmax and the amplitudes Vflat of the outer flat parts. The dynamical state of the gas disks could also be determined in detail from the radio observations. The four luminosity and three kinematic measures allowed the construction of 12 correlations for various subsamples. For large galaxy samples, the Mb,iR-logWiR,I correlation in conjunction with strict selection criteria is preferred for distance determinations with a 7% accuracy. Galaxies with rotation curves that are still rising at the last measured point lie systematically on the low-velocity side of the TF relation. Galaxies with a partly declining rotation curve (Vmax>Vflat) tend to lie systematically on the high-velocity side of the relation when using WiR,I or Vmax. However, systematic offsets are eliminated when Vflat is used. Residuals of the Mb,iB-log(2Vflat) relation correlate consistently with global galaxy properties along the Hubble sequence like morphological type, color, surface brightness, and gas mass fraction. These correlations are absent for the near-infrared Mb,iK'-log(2Vflat) residuals. The tightest correlation (χ2red=1.1) is found for the Mb,iK'-log(2Vflat) relation, which has a slope of -11.3+/-0.5 and a total observed scatter of 0.26 mag with a most likely intrinsic scatter of zero. The tightness of the near-infrared correlation is preserved when converting it into a baryonic TF relation that has a slope of -10.0 in the case (Mgas/LK')=1.6 while a zero intrinsic scatter remains most likely. Based on the tightness of the near-infrared and baryonic correlations, it is concluded that the TF relation reflects a fundamental correlation between the mass of the dark matter halo, measured through its induced maximum rotational velocity Vflat, and the total baryonic mass Mbar of a galaxy where Mbar~V4flat. Although the actual distribution of the baryonic matter inside halos of similar mass can vary significantly, it does not affect this relation.