What's the difference between "successive" and "consecutive"?
First note that successive appears as a synonym of consecutive in dictionaries. (see Merriam Webster's entry here).
Now compare these examples that I chose at random and extracted from the Corpus of Contemporary American English (COCA):
Here is what I observe in the examples (I hope I was lucky in my random choice of them):
In the examples that use consecutive, the fact that the events happened in a row without interruption seems to be something that the author wanted to emphasize.
However, in the examples that use successive, the fact that the events occur after each other with no interruption seems to play a secondary role. Notice that you can remove successive from some of these sentences and the meaning is not affected too much. If you remove consecutive, the impact is in general higher.
I think there isn't any difference in denotation. I suspect that "successive" is more apt to be used in a casual nontechnical context, and "consecutive" when the subject involves math or is otherwise technical.