Publishing the Lesson using the large Publish button will update only the stand-alone Lesson with the changes, and not the Lesson as part of a Module(s) (or, if the Lesson is only part of a Module, this will Publish it as a stand-alone Lesson):
Publishing the Lesson in this way will not Update any associated Modules - just the stand-alone Lesson
Clicking the 'Publish the latest changes by updating the published module' link and then the 'Update to Latest' button will apply this update to the Lesson within the Module:
Updating the Module will only apply the changes made to the Lesson within the associated Module. Other Modules, or stand-alone Lessons will not be updated.