Spiking Neural Networks (SNNs) are considered promising brain-inspired energy-efficient models due to their event-driven computing paradigm.The spatiotemporal spike patterns used to convey information in SNNs consist of both rate coding and temporal coding, where the temporal coding is crucial to biological-plausible learning rules such as spike-timing-dependent-plasticity.The time-based training strategy is proposed to better utilize the temporal information in SNNs and learn in an asynchronous fashion.However, some recent works train SNNs by the time-based scheme with rate-coding-dominated loss functions.In this paper, we first map rate-based loss functions to time-based counterparts and explain why they are also applicable to the time-based training scheme.After that, we infer that loss functions providing adequate positive overall gradients help training by theoretical analysis.Based on this, we propose the enhanced counting loss to replace the commonly used mean square counting loss.In addition, we transfer the training of scale factor in weight standardization into thresholds.Experiments show that our approach outperforms previous time-based training methods in most datasets. Our work provides insights for training SNNs with time-based schemes and offers a fresh perspective on the correlation between rate coding and temporal coding.Our code is available at https://github.com/zhuyaoyu/SNN-temporal-training-losses.