EDI IS TECHNOLOGY BY USING THAT WE R CONVERTING THE DATA
ONE FORM TO ANOTHER FORM
ALE IS INTERFACE BY USING THAT U CAN  CREATE ALINK BETWEEN 
TWO SYSTEMS .BY USING U CAN TRANSFER THE DATA

EDI is used to transfer data between two organizations which
might be SAP or non SAP system.
ALE is used to transfer data with one organization(for its
different plants).It need to be SAP system in both plants.

EDI:
edi is electronic data interchange is exchange the data by
electronically from one system to the another  system that
is weather is document or anything.ex:if you send the
purchase or der from the (sender) system that means outbound
system that is recieved to sales order to the inbound
system(Reciever)
so that means that document is changed by electronically
from  the outbound system to the inbound system.

ALE:

Application link enabling it provides the link between the
two systems that is the sap or non-sap or third party
systems within the distributed systems only. ex: if u send
the purchase order from the outbound system the inbound
system also recieves the same purchase order . that means
there is no change. so changes not possible in ALE.

In both ALE and EDI , we interchange data between two 
systems.This interchange of data between the systems is 
facilated by the intermediate documents(IDOCs).Both ALE and 
EDI make use of IDOCs.
In case of ALE the interchange of data is between two SAP 
systems.
Whereas in EDI the data is interchanged between SAP and a 
NON-SAP system.
These technologies are used mostly in case of transactional 
data.

However, bothe technologies can be used to send data from 
one system to another with any kind of systems involved( 
SAP to SAP or SAP to non SAP or SAP to third party).
In EDI transfer is Synchronous
While in ALE it is Asynchronous, means sender sends the 
data withhout knowing if reciever has recieved it in 
correct form or not.
ALE interface uses EDI interface when communication is 
between SAP to non SAP systems.
In EDI data is sent in file format mainly
In ALE it is not