Serializing is about moving structured data over a storage/transmission medium in a way that the structure can be maintained. Encoding is more broad, like about how said data is converted to different forms, etc. Perhaps you could think about serializing being a subset of encoding in this example.
With regard to a web service, you will probably be considering serializing/deserializing certain data for making/receiving requests/responses – effectively transporting “messages”. Encoding is at a lower level, like how your messaging/web service type/serialization mechanism works under the hood.