Learn English – Assemble, Convene A Conference

Using the OALD for definitions, a symposium is:

a meeting at which experts have discussions about a particular subject; a small conference

A conference is:

1. a large official meeting, usually lasting for a few days, at which people with the same work or interests come together to discuss their views
2. a meeting at which people have formal discussions

A symposium is usually used to describe a small conference on a single subject. For example, a series of lectures on a single day might be called a symposium.

A conference is usually large, possibly taking up many rooms in a hotel or a convention center. It usually takes up several days. It can also describe a single, small meeting--for example,

He was in conference with his lawyers all day.

Short answer: no conferences belong in conference rooms. Meetings you can potentially have anywhere.

conference from Latin conferre (bring together)

which is almost the same like meeting

Meeting is more of an encounter.

A conference (a bringing together) implies more effort. Usually a conference also takes longer than a (relatively quick) meeting.

So a meeting room might just be a simple room for a quick meeting. (all meeting rooms these days, at least at my workplace, seem to have conference capable phones in here anyway, so the distinction is blurry)

A conference room might be more sophisticated with video conferencing equipment or dedicated presentation facilities.

You can have a meeting in a conference room, as you can meet in any other room say the kitchen or bathroom.

You could also have a conference in the canteen, or the bathroom even though I don't think that is considered best practice.

So having a conference in a meeting room might not make sense, since the meeting room might be to small and lack the proper equipment. Speaker facilities, video conferencing facilities.