It's still not clear to me what the difference is between a Meeting and a Conference. It seems like these words are mixed up in the documentation. The word "meeting" is used in the documentation of the conferences , and the word "conference" is used in the documentation of meetings, which makes it very confusing. So what is actually the difference between a meeting and a conference? And what is the relation between them?

Commonly a meeting is scheduled (i.e. a meet me arangement) where people dial into a meeting bridge.
Conference is more ad-hoc where A and B are talking and one of them adds in C through some sequence of actions (hold, call, join/answer or answer/join)
Both result in a multi party conversation being possible.
Meetings tend to have some management interface allowing operations like lecture mode, muting parties that conferences do not have available equivilents.
Meeting managment UIs tend to have some mechansim to dial out to a participant(s) to add them to the meeting, but that is typically done very differently than you would see in an ad-hoc conference situation. i.e they are called and when they answer they are joined into the meeting automatically - although there is screening capabilities in some meeting systems allowing the moderator to avoid adding answering machines and the like into conferences.

However, as you travel the world and work with non-English language native speakers, the terminology becomes used however the writer/speaker is familiar with the words themselves resulting in confusion.