EDI stands for Electronic Data Interchange and means transfer of structured information according to a given format. Information transfer between companies is often stock balance, catalog information, order, order confirmation, advanced shipment note and invoices.

EDI is a elaborated to structure information. A wildly spread standard is EDIFACT which is administrated by UN/CEFACT, a part of the UN.
The XML-format is getting a larger implementation of standards such as ebXML which also is sponsored by UN/CEFACT.
The automotive industry primarily uses Odette for information exchange, which is a version of EDIFACT, while the organization Sveriges kommuner och landsting stand behind a different version that goes by the name Single face to Industry (SFTI). 
In North America the mostly use the ANSI X12-standard. Apart from standardized formats like the once mentioned above there are some Proprietary formats in form of flat filer or normal Excel-documents. In Zwapgrid we often work with UBL. Universal Business Language.


Integration in our world, means that you connect systems so that they can share information.


API stands for Application Programming Interface and is a very simplified way of in a structured way receive and send data, commands to and from a system and so forth. There is a number of different methods for this (SOAP, REST among others) but every API is unique for each system. 
Many times user name, password as well as a so called API-token is required to be able to get data through a API. These work as keys to make sure that the information that is being collected/updated is done thorough a trusted application or person.