Yes, to clarify this a little. It's a complex area and people can make mistakes out of a lack of knowledge, and airlines don't go out of their way to explain EC261 clearly.

For cancellations at short notice - under 2 weeks - then compensation is potentially payable regardless of a refund request. But if you cancel you do yourself out of the rebooking protections in many circumstances (there are some exceptions)
For delays - on the day obviously - then refunds removes compensation in most (but not all) cases and also you lose rebooking protections.

Hence the advice here is always to seek advice before going down the refund route, unless you 101% understand the legislation. Let's put it this way, I think I do understand the legislation and yet I would not immediately react in an irrop to a refund - I would take a few minutes to think it through. It's very easy to make mistakes here.

There is a bit more context in the disruption signposts thread, indicated upthread.