This question boils down to one thing: are you part of the transaction or not?
Data Integration grew out of the adoption of relational databases and the need to move information between them. Typically, data integration is batch-orientated and deals with data at rest. In other words, the process that created the data has already completed.
Application Integration, on the other hand, deals with integrating live operational data in real-time between two or more applications. Typically an “event” will occur. For instance, when a customer places an order, this triggers an integration flow that updates and enriches data in other applications in real-time.