Empirical evidence is a type or category of evidence.
So you're incorrect.
When someone demands empirical evidence for a claim such as "Jesus rose bodily from the grave" they are demanding evidence that is observable, repeatable, and testable. A very specific and a very particular kind of evidence. They aren't just asking for any kind of evidence. If that were the case, then they would accept what Christians traditionally have appealed to as evidence, the accounts of His life death and resurrection found in the New Testament documents.
What such people who make such demands are doing are narrowing the criteria for evidence down so far as to render it impossible for the Christian to meet their terms. Sometimes it is a form of moving goalposts where they initially start out by saying something like,
"Well show me some evidence and I will accept your claims!"
Once the Christian does this, they will respond by saying something like,
"Well, it is not empirically verifiable evidence!"
This is a classic example of moving goalposts. The first request was met, the ball was going through the goalposts, but then the goal is moved back so that the ball cannot go through.
Sometimes the challenger will make demands for evidence that he knows cannot even in principle exist. Once again, we can use the above as an illustration. In principle, empirical evidence cannot exist for the claim that Jesus rose bodily from the grave and yet they ask for it and when it can't be given, they congratulate themselves with a pat on the back.
