Chromosome conformation capture (3C) and fluorescence in situ hybridization (FISH) are two widely used technologies that provide distinct readouts of 3D chromosome organization. While both technologies can assay locus-specific organization, how to integrate views from 3C, or genome-wide Hi-C, and FISH is far from solved. Contact frequency, measured by Hi-C, and spatial distance, measured by FISH, are often assumed to quantify the same phenomena and used interchangeably. Here, however, we demonstrate that contact frequency is distinct from average spatial distance, both in polymer simulations and in experimental data. Performing a systematic analysis of the technologies, we show that this distinction can create a seemingly paradoxical relationship between 3C and FISH, both in minimal polymer models with dynamic looping interactions and in loop-extrusion simulations. Together, our results indicate that cross-validation of Hi-C and FISH should be carefully designed, and that jointly considering contact frequency and spatial distance is crucial for fully understanding chromosome organization.