What is the difference between 立つ and 起つ?
起つ one of the rare readings found mainly in novels and other aesthetic writings. Specifically, 起つ is occasionally used to mean to rise up (in revolt), to stand up (e.g., for a captive princess), etc. Some people may use it to refer to something else according to their preference and creative sense.
In serious news articles and such, we use 立ち上がる, 決起する or 蜂起する for this meaning. The usage of 起つ is not something we learn at school, and you don't need to use 起つ unless you're interested in creative writings.