In your conference presentations you can use any title you like (as long as it is subject appropriate). Make sure you do not publish the same paper twice (in a journal and in conference proceedings). But having the title of your presentation listed in proceedings is not the same as having your paper published in proceedings. Some conferences publish abstracts of talks. This is again different from paper publications.
Edit. In view of your edits: Typically, an extended abstract is still not a paper (unless your paper is so short that it can fit entirely in an extended abstract). A typical extended abstract is similar to the introduction to a paper. Hence, publishing a typical extended abstract in conference proceedings (under any title) does not preclude you from publishing the corresponding paper separately, in conference proceedings or in a journal. For the record: My area is pure math. I have done what I described above in the past with my papers. I also have served several times as an editor of proceedings publishing extended abstracts. One thing in your question bother me: the fact that your conference covers all branches of math. With few exceptions (such as ICM, EMS or AMS meetings, none of which publishes extended abstracts), this is a sign of a predatory conference.