As far as I am concerned, residual activity is when you do some assay (like thermostability, heating the enzyme up to a determined temperature), and then measure the activity in optimal conditions. For example: You have a hydrolase with optimal temperature of 45 oC. You can heat for, let´s say, 70 oC for x minutes and then test the activity at 45 oC. That would be the residual activity, and the same could be done for pH, etc.
Relative activity you consider a proportion to something else. You could, for example, use relative activity for your enzyme using the maximum activity measured as 100%, and then you have a graph in relative terms. If your enzyme presents a maximum activity of 1500 U/mL, that would be your 100%, and anything below that would be proportional to 100%.
Both residual activity and relative activity are relative to the initial enzyme itself.
However, residual activity pays more attention to the changes in activity after some treatments, such as heating, changing pH, etc. Relative activity is just relative to the parent.