Conversation - Conversation is a group talk. It is a talk between any number of people. It may be a talk in between even two people, or maybe even thousands of people talking among one another. This may be a group talk as well as personal talk.
Dialogue - Dialog is also a talk among people. It is a talk among basically two people. That is why dialogue is a conversation but a conversation is not always a dialogue, because it maybe even more than two people, as earlier I said, conversation may be a talk among hundred people also.
1. The students of Class IX B were in big conversation with each other, so many at once.
2. Me, Samiul and Rahul were in conversation last evening, about the exhibition.
3. Sameer and his group were in conversation about their project.
1. Husband and wife maybe in tough dialogues, it seems to be a quarreling fight.
2. I and Sam were dialoguing with each other yesterday.
3. She and Anil look to be very serious in the dialogue among themselves, is the matter alright?