Multi-modal entity alignment (MMEA) aims to find the equivalent entities between multi-modal knowledge graphs (MMKGs). Current MMEA methods follow the ''embed-fuse-compare'' paradigm and show decent performance improvements on several public datasets. However, this paradigm may fail to fully address inconsistencies across different modalities, resulting in instability and sub-optimal performance. In this paper, we propose a novel paradigm called ''embed-fuse-assign'', which transforms MMEA into a multi-modal assignment problem. First, we prove that multi-modal entity alignment can be turned into assignment problems and identify that obtaining correspondence scores is the crucial step. Then, we devise a novel Explicit and Implicit multi-modal Entity Alignment (EIEA) algorithm, which classifies modalities into explicit and implicit categories based on the need for joint neighborhood information, designs modality-specific embedding and correlation scoring mechanisms, and derives alignment results by integrating correspondences across all modalities. Finally, we introduce a conflict-aware soft pseudo-labeling method to further optimize semi-supervised learning for implicit modality. Extensive experiments have demonstrated that our proposed paradigm and algorithm achieve the state-of-the-art performance on five real-world MMEA datasets. The source code and datasets are released at https://github.com/Bubble-bubble77/EIEA.