A press conference is a means of conveying more information than can be carried in a single press release. It is also a way of occasionally utilizing senior officials in the election administration and putting them before the public (in the form of the media) to explain the electoral process.
Broadcasters like press conferences, of course, because a press release will only give them 'white copy' - that is a story with no picture or sound. At a press conference broadcasters will be able to record and film. If a customized 'mee02e' is available then this will make the practical requirements of broadcasters easer to meet. Otherwise, the organizers of a press conference will have to allow for the needs of television and film crews, radio journalists and photographers.
The usual format for a press conference is for a representative of the electoral authority to make a statement, which is then open to questions from journalists. The press conference should be chaired by someone other than the official making the statement. It helps to establish a clear time for the conference (and to start promptly - journalists have deadlines). The chairperson should ensure that journalists from a variety of different media, with different political viewpoints, have a chance to ask questions. Broadcast journalists will insist on the chance to ask their question (because they will want it broadcast). That is reasonable, but no one should be allowed to hog the questioning. Sensitive and balanced chairing will create a trust between the media and the authority holding the press conference.
A media briefing is usually something rather different. This will normally not be for broadcasting and sometimes is completely 'off the record'. If the latter, then the strict rule is that the person doing the briefing may not be identified. Politicians brief 'off the record' the whole time. It is scarcely possible to envisage any circumstances where it would be proper or appropriate for an electoral official to do so. With detailed briefings, as with other information for the media, invitations should be issued to all media, regardless of political persuasion or ownership.