RD is about comparing two groups that are very similar except for the treatment because the treatment depends discontinuously on come cutoff. For example, those with a test score of 1499 don't get to go college and those with 1501 do. The underlying ability of these two groups is probably similar enough, so the post-college wage comparison near 1500 has high internal validity because the only difference between the two is the college education. Everything else is constant. Unfortunately, RD does not have very much to say about what happens at a score of 1357 or 1600.

DID is about comparing two groups that could have some pre-existing difference on top of treatment, but the effect of that difference is assumed to be constant over time. When you take the first difference of the outcome for each group over time, the time-invariant effect is subtracted out and doesn't contaminate the comparison in the second difference.

So RD requires different assumptions and less data that DID, but it estimates a more local effect around the cutoff. DID requires panel data and is less local in some sense.

In the extreme case when the number of periods before and after the treatment is very large, we could do an RDD with time as the running variable and the difference between treatment and control groups as the outcome. I don't think it is possible to go in the other direction.

RD is about comparing two groups that are very similar except for the treatment because the treatment depends discontinuously on some cutoff. For example, those with a test score of 1499 don't get to go college and those with 1501 do. The underlying ability of these two groups is probably similar enough, so the wage comparison for those on either side of 1500 has high internal validity because the only difference between the two is the college education. Everything else is constant. Unfortunately, RD does not have very much to say about what happens at a score of 1357 or 1600.

DID is about comparing two groups that could have some pre-existing difference on top of treatment, but the effect of that difference is assumed to be constant over time. When you take the first difference of the outcome for each group over time, the time-invariant effect is subtracted out and doesn't contaminate the comparison in the second difference.

So RD requires different assumptions and less data that DID, but it estimates a more local effect around the cutoff. DID requires panel data and is more global in some sense.

In the extreme case when the number of periods before and after the treatment is very large, we could do an RDD with time as the running variable and the difference between treatment and control groups as the outcome. I don't think it is possible to go in the other direction.