Hi,
Basically you can consider Share as just being a UI that displays Alfresco content.
All the content, including your node and their renditions.
If you want to retrieve a thumbnail from an Alfresco webscript where you're already authenticated, have a look at
/alfresco/s/script/org/alfresco/repository/thumbnail/thumbnail.get
It's obviously possible to retrieve it from Alfresco code (like within one of your custom webscript) too depending on your use case.