It's a little difficult to answer precisely without more context, but 'testing' is usually an activity which is done prior to putting something into service, and may also done once it is in service, in order to verify correct operation. 'Deploying' something is the act of putting that something into service to do whatever function it is intended to do. Normally deployment happens after after testing.
For any new discrete operation, I create logic and simulate/test all of the associated conditions in a PLC that is hanging on my office wall (development). Once I am confident that everything works as designed, I migrate the operation to the running system (deployment). Once it is there, then I usually have to do some amount of testing, but as it was tested during development confidence is high that everything works. Anything that is not tested is not certain to work when called on, no matter how simple it seems.
The usual definition of "deploy" refers to a military or police operation, in plant design you can have
1. Design
2. Multiple Design Reviews
3. Purchase
4. Hardware Shipping
5. Installation/Construction
6. Construction Completion
7. Electical and Instrument Checkout including Preliminary Field Check out of Control Hardware and
Software
8. Pre-Start up Testing (Includes Many parts of the project) and Checkout
9. Start up Testing
10. Prelininary Operation
11. Plant Commisioning and Operator Training
12. Handing the Keys to the Owner...for his performance testing and additional training.
13. Process Evaluation and Debugging, Identification of under performing processes, etc.
Any Automation Control hardware has it own testing and shipping cycle ...
