There are many differences between IDOCs and BAPIs. BAPIs in 3.1 are synchronous; in 4.+ they can be asynchronous (and I believe they then drive certain ALE/IDOCs). BAPIs are called from the outside-in.  That is, an external program invokes a BAPI that gets data from SAP to display or updates data in SAP.  The BAPI [...]

ALE (click here for documentation) ALE is SAP proprietary technology that enables data communications between two or more SAP R/3 systems and/or R/3 and external systems. When a new enterprise resource planning (ERP) solution such as R/3 is implemented, companies have to interface the ERP system with legacy systems or other ERP systems. ALE provides [...]