Alfresco Explorer and Alfresco Share both are the web interfaces to alfresco. Alfresco Explorer is the old web client. This old webclient and the repository are in the same web application. It was the only webclient for many years. This webclient is not being actively developed and There aren't any new updates in place for this webclient as it is not on the roadmap of alfresco. Hence, you should not use the old webclient - Alfresco explorer.
Alfresco Share is the new and modern web client and is the one being actively developed. You should actively use this web interface instead of alfresco explorer and should have end-users also use this only. If you are planning to make any customizations then Alfresco share should be customized.