What is static complexity?
Complexities in this context could be divided into dynamic and static: 


Dynamic complexity is an attribute of the execution of a program with the string as an input. For example, the time or space complexity of a Turing machine to accept or reject a string.
Static complexity is an attribute of a program that receives the string as input but not its execution. As you stated, Kolmogorov complexity is a static complexity since it is the length of the shortest program that creates the given string, an attribute that implies nothing about the execution of the program.