The traditional term that is the closest to what the OP seems to have in mind was, as WS2 already pointed in a comment, chairman, which was treated as gender-neutral (so that addressing somebody as Madam Chairman was not perceived as incongruous). Over the last fifty years or so, the arguments that such compounds containing -man cannot be genuinely gender-neutral have resulted in chairman being replaced with chairperson or just chair, and these are now the most frequently used terms for somebody who runs, or chairs, a meeting of a deliberative body, i.e. who opens it, ensures that it proceeds according to the announced agenda and the applicable rules, that those who are entitled to speak at it are able to do so in an orderly way, that the votes are taken at the appropriate times, and so forth. The chairperson may also do some of the work that needs to be done in preparation for the meeting, but that may also be the responsibility of somebody else in the organisation (i.e. it is not a part of the definition of the chairperson). The preparation of the minutes of a meeting is also usually the responsibility of somebody else (who may be called the secretary of the organisation).
In some organisations, it may be customary to refer to and address a person who chairs its meetings according to the person’s role in the organisation (rather than the specific role in the meetings): for example, if the person chairing a meeting is the president of the organisation, the person may be addressed in the course of the meeting as the president, rather than the chairperson.
The other terms offered on this page have similar, but somewhat different meanings.
Somebody may be invited to make a presentation to a deliberative body to help it reach a decision on a particular matter; that person may be called a presenter, but that is a role distinct from that of a chairperson. A presenter does not have the power to run the meeting as a whole (unless the presentation is the entirety of the meeting and the audience is not a deliberative body at all, but that does not seem to be the scenario that the OP has in mind).
Moderator and facilitator are relatively new terms that are sometimes used in the contexts in which chairman or chairperson would have been used in the past, but they are better suited to the debates and negotiations that are not meant to lead to an authoritative decision. The motivation for introducing these terms is that they imply a less hierarchical structure than chairperson: this makes them appropriate for some kinds of meetings, but inappropriate for those in which a formal binding vote needs to be taken, and somebody needs to have the power to ensure that it is taken in accordance with the applicable rules.
The term meeting owner, mentioned by the OP, is not normally used in ordinary communication. I suspect that the OP has heard it in the context of some software for scheduling meetings in which the user so designated has greater privileges (including e.g. the ability to invite the participants and set the agenda) than the ordinary participants. Whatever usefulness the term may have as an explicitly defined technical term in that limited context, it would be odd to use the it outside that context (and potentially insulting to the members of the deliberative body in question, who are unlikely to think of the chairperson as owning the meeting).