Plasmonic nanostructures have become the most promising candidates for biosensing applications because of their miniature sizes, ease of integration, and high-throughput detection. Both propagating and localized surface plasmon modes in the nanostructures have been used for sensing and biomolecular detection. However, to maximize the biosensing potential of nanostructures, the choice of an optimized sensing detection strategy among two plasmon modes depends on the relationship between the biomolecule sizes and field decay length of plasmon modes. Here, we propose and investigate plasmonic coupling on a single-crystalline gold film, wherein there are two distinct optical modes, a gap mode (localized surface plasmon) originating from the parallel coupling of a nanoring and a surface lattice mode (propagating surface plasmon) originating from the anti-parallel coupling of a nanoring in an array. The sensing performances of the above two modes are thoroughly investigated and compared by considering two aspects, i.e., bulk and surface sensitivities. It is demonstrated that there is a reciprocal relationship between bulk and surface sensitivities for two modes, which also illustrates that the surface sensitivity is indispensable to fully describe the sensing performance of nanostructures. Furthermore, due to their different decay lengths, the gap and surface lattice modes on a single optical substrate can achieve simultaneous detection of target analytes with various sizes. Therefore, we can provide a high performance sensing platform based on a metallic nanoring array for a broad range of biomolecules with various sizes.