EDI means Electronic Data Interchange, API means Application Programming Interface. Newer applications on the Internet tend to offer APIs, older applications EDIs.
The main difference is: 
EDI usually involves files being transmitted from one system and then imported into the other, whereas use of an API indicates that the applications are talking directly to each other. That's it.
For 99% of businesses they're functionally the same, and which costs more will come down to what tools your provider already has lying around. Anyone pushing one over the other is probably trying to sell you something. For me, they both do the same thing. They take a message from me, and do something; or let me get a message from you, and do something.
But why would I want to set up an interchange with another business? There are four big reasons:
1) I do a lot of work with someone, and I want to cut down the time spent entering data.
This is the big driving force for integrations to big trading partners (such as Foodstuffs, Coles, Mitre10, Fletchers, Ravensdown, Bunnings, Placemakers). I do so much work with this person I want to automate it. By doing this, it:
In this way, setting up interchanges is a good way to keep my competitors away, but it also locks me in (because I've sunk a cost into this relationship.). But this isn't so different from every business I have, and if spending upfront can save me a FTE per year, the business will quickly recoup the cost.
2) Allows me to offer better data to my customers.
This is the driving force I see behind logistics integrations. Coles might order you to enter things into their system just so, which lets their supply chain manage itself completely, but just the same I could integrate my system to Mainfreight, GoSuiteSpot, or CourierPost so I can give good tracking updates to my customers when they buy from my website.
The simplest end of this is just letting my customers know the tracking number on their order, so they know when their parcel will arrive.
The motivators I see here are:

3) It makes all of the information accurate.
People mishear things and the best typists still make mistakes. But the computer sends exactly what it is told to send. The number of errors drops, and I can see the information I need.
4) Timeliness
Timeliness can be a big one – both EDIs and APIs offer big improvements over manual processes.
Why? Because there's no more chance that someone forgets to hit send on the invoice, or that the mail gets lost. While we treat emails as being received, the truth is that they aren't always received (https://blog.returnpath.com/email-deliverability-still-plagues-commercial-email-senders-worldwide-only-81-of-email-reaches-the-inbox/).
Forgive the old article in the link but email receipts just like physical mail aren't guaranteed. And plus people get a lot of spam, and a lot of fake requests. There are lots of reasons this can go wrong and they all cost money.
This has been a very basic primer on Automation via EDI or API, future posts will dive more into some automatic options.
About the Author: Will HowardWill joined Focus in 2015, formerly working directly for MYOB. He is a certified MYOB EXO and MYOB Advanced consultant with a passion for reporting, data automation, and making business life easier through process control. To engage his services, reach him via our contact page.
Don’t get hooked with fraudulent emails - part 3
30 September 2019
Don’t get hooked with fraudulent emails - part 2
29 August 2019
Don’t get hooked with fraudulent emails - part 1
07 August 2019
How to protect yourself from cyber-attacks
31 May 2019
Exosoft Tip: Invoicing via JIBE
18 March 2019
Exosoft Tip: Markups in JIBE
14 March 2019