The usual gist is that the IT is done to "groom the system" until it works and the ST is designed to prove to the customer that the system works as required.
Something has bothered me until I've realized that I've felt that there's a little bit of hypocrisy in the distiction between the IT for internal use and the ST for the external show - me being for the whole length of my career on the customer's side. Never more. There is no hypocrisy - just plain business. I do my IT and then do the ST to sell you my product. You do your IT to integrate my product into your product and then do ST to further sell your product to the next guy etc etc.
Just like the VAT tax - the last one pays the bill and it is the ultimate customer - the user that has only IT to do and then use the system for the length of its lifecycle. There is no ST here because there are no requirements to falsify.
So that's crucial for the understanding that there is a kind of "Final Integrator" that is the User or someone working on his/her behalf and the type of Systems Integration that is done by the Final Integrator is very distinct from one that's done by any kind of Systems Developer. I propose to name this two types of integration the System Integration to Sell (or Ship) and the System Integration to Use and discuss them separately.