Question: Strategy pattern and Dependency Injection both allow us to set / inject objects at run time. What is the difference between Strategy pattern and Dependency Injection?

Answer: 
DI and Strategy work in the same way, but Strategy is used for more fine-grained and short-lived dependencies.

When an object is configured with a "fixed" Strategy, for example when the object is constructed, the distinction between Strategy and DI blurs. But in a DI scenario it is more unusual that the dependencies of objects change during their lifetimes, while this is not uncommon with Strategy.

Also, you can pass strategies as arguments to methods, while the related concept of method argument injection is not widespread and mostly used in the context of automated testing only.

Strategy focuses on intent and encourages you to create an interface with different implementations that obey the same behavioral contract. DI is more about just having an implementation of some behavior and providing it.

With DI you can decompose your program for other reasons than just to be able to swap parts of the implementation. An interface used in DI with only one implementation is very common. A "Strategy" with only one concrete implementation (ever) is not a real problem but is probably closer to DI.
You can use DI as a strategy pattern, so you can swap in the algorithm that is needed for each customer, but DI can go beyond that as it is a way to just decouple the parts of an application, which wouldn't be part of the strategy pattern.

It would be risky to say that DI is just a renamed strategy pattern as that starts to dilute what the strategy pattern really is for, IMO.