Concurrency: Is it order-independability or interruptibility of tasks?
Concurrency is working with tasks that may run simultaneously.  In my experience, when this term is used, the main focus is on correctness: making sure a system works as intended.

One way of doing that is to impose additional constraints on the system and ensure that they are always met.  Order independence and interruptability are examples of two such constraints.  You may want them to hold for your concurrent system.   But they are not required properties of concurrent systems in general: for many concurrent systems, they do not hold and do not need to hold.  

For instance, in MySQL, you can configure to what extent you want your transactions to be isolated, with full serializability (order independence) as the highest level.