Difference between EDI and ALE IDOCS

ALE (Application Linking and Embedding) is the transport mechanism for remotely calling functions (RFC's, BAPI's, etc.) and is an SAP technology. It is basically used to transfer IDOC with in the R3 distributed system and if you want to reproduce data amongst trusting systems to save a terminated copy of the IDoc data. 

To send the data between the two systems you would have to use ALE. In ALE data is transfer from memory to memory. It usually supports Trfc ports and data will be stored in memory buffer, and used R/3 connection. 

EDI (Electronic Document Interface) is a set of instructions (ANSII X-12/EDIFACT) that designate the semantics of message connections amongst to "EDI" aware but technically different systems. In SAP you would create an IDOC (Intermediate Document) and pass it off (map) to some third party EDI subsystem (Business Connector/Cross Worlds...) for the actual EDI message exchange. 

It is basically used to transfer IDOC from R3sytem. If you want to send data to an external partner you would need EDI. Although if you want to send data between SAP to non-SAP system or vice versa you would have to use EDI. In EDI the transfer of data is between IDOC to a flat file. It usually used file ports; there can be multiple messages formats and uses TCP/IP connections. Hope this article might help you to clarify the difference between the ALE and EDI.