Valgrind: what is the difference between a store and a modify?
This sounds like a question about the terminology that Valgrind happens to use, more so than a question about fundamental aspects of computer science.  I suggest you ask on a Valgrind support forum if you want an authoritative answer.

Based on your examples, it looks like the most likely answer is that the Valgrind folks are using the word "store" to mean "an operation that writes to memory, overwriting in a previous value with a new value that does not depend upon its previous value" while they mean "modify" to mean "an operation that writes to memory, updating its value to a new value that may depend upon the value previously stored in that location".  Only Valgrind folks can confirm authoritatively whether this is actually what they mean.