Universal distance modes from DESI BAO and Type Ia supernovae: what do cosmological rulers actually measure?

We use an SVD decomposition of the low-redshift distance measurements from DESI BAO and three Type Ia supernova compilations to identify the leading linear directions probed by the data and to localize the tension with the LCDM CMB-anchored predictions. The leading direction V 0 -- whose data amplitude we denote c 0 -- is, to high accuracy, a measurement of Omega m h 2: the projection of the data on V 0 probes essentially this one CMB-derived parameter combination. BAO constrains this parameter more tightly than the CMB itself; the three SN compilations do not. In every extension of LCDM we consider, the leading measurable direction remains V 0, and it is where most of the tension with the CMB resides. In the w0-wa extension a second direction V 1 becomes measurable and provides an independent test of dynamical dark energy; the data show no significant tension in this direction. The only other beyond-LCDM extension that opens a genuinely new measurable direction is spatial curvature, and only marginally and only for BAO; both measurable directions then independently prefer positive spatial curvature, though the second direction is poorly constrained.