With the rapid advancement in remote sensing Earth observation technology, an abundance of Time Series multispectral remote sensing Images (TSIs) from platforms like Landsat and Sentinel-2 are now accessible, offering essential data support for Time Series remote sensing images Change Detection (TSCD). However, TSCD faces misalignment challenges due to variations in radiation incidence angles, satellite orbit deviations, and other factors when capturing TSIs at the same geographic location but different times. Furthermore, another important issue that needs immediate attention is the precise determination of change moments for change areas within TSIs. To tackle these challenges, this paper proposes Multi-RLD-Net, a multi-task network that efficiently utilizes difference features to explore change areas and corresponding change moments in TSIs. To the best of our knowledge, this is the first time that using deep learning for identifying change moments in TSIs. Multi-RLD-Net integrates Optical Flow with Long Short-Term Memory (LSTM) to derive differences between TSIs. Initially, a lightweight encoder is introduced to extract multi-scale spatial features, which maximally preserve original features through a siamese structure. Subsequently, shallow spatial features extracted by the encoder are input into the novel Recursive Optical Flow Difference (ROD) module to align input features and detect differences between them, while deep spatial features extracted by the encoder are input into LSTM to capture long-term temporal dependencies and differences between hidden states. Both branches output differences among TSIs, enhancing the expressive capacity of the model. Finally, the decoder identifies change areas and their corresponding change moments using multi-task branches. Experiments on UTRNet dataset and DynamicEarthNet dataset demonstrate that proposed RLD-Net and Multi-RLD-Net outperform representative approaches, achieving F1 value improvements of 1.29% and 10.42% compared to the state-of-the art method MC2ABNet. The source code will be available soon at https://github.com/lijialu144/Multi-RLD-Net.