Literally "realize" means "make real". So "many projects have been realized" means many "ideas for projects" have been turned into "actual, real projects."
While this phrase often implies the projects were finished, it does not have to. The meaning of "reaize" isn't finishing the project: it is changing something that is not a project (it is only an idea) into a "real project" with workers, plans, money, resources etc.
Both "execute" and "carry out" emphasize something different: bringing an already-real project to completion.