Once-through molten salt reactors have the advantages of easy availability of fuel, nuclear nonproliferation, and low technical difficulty. It is expected to be the earliest commercial molten salt reactor fuel cycle mode. The current research on the neutronic performance of the once-through fuel cycle mainly focuses on the thermal spectrum range, and broader spectrum research needs to be carried out further. In particular, the fuel utilization characteristics of molten salt fast reactors in once-through fuel cycle are not yet clear. In addition, small modular design is one of the trends of molten salt reactor development, and small modular design under thermal and fast spectrum has different advantages and needs further comparative analysis. In this paper, the single lattice, bare reactor, and core with reflector models are used to compare the neutronic performance in once-through fuel cycle from thermal to fast spectrum, which includes burnup, variation of fuel salt composition and volume with burnup, temperature reactivity coefficient, neutron irradiation lifetime, and small modular size. The results show that the burnup increases first, then decreases, and then increases again with the increase of the average lethargy causing fission (EALF). For small-scale molten salt reactors, the difference in fuel utilization under thermal and fast spectra is small. However, for large-scale reactors, the burnup under fast spectrum is significantly higher than that under thermal spectrum. When the EALF is large enough, and the neutron loss ratio is small enough, the breed-and-burn (BNB) fuel cycle mode can be realized, and then, the fuel utilization will be significantly improved. In the fast spectrum reactors, the HN and volume of molten salt change violently because of the longer burnup period. Based on the infinite single lattice model, the temperature reactivity coefficient increases first, then decreases, and increases again with EALF. It is negative over the entire energy spectrum. In addition, the small modular designs are discussed by the bare reactor model, and the neutron irradiation lifetime of the materials is analyzed by the core model with a reflector.