Formal:
* Convo: This is a common informal abbreviation.
* Chat: This can be used for both informal and formal conversations.
Informal:
* Talk: This is a general term and can refer to any kind of discussion.
* Chit-chat: This refers to light, informal conversation.
* Dialogue: This is more formal, but can be used in informal contexts as well.
The best short form will depend on the specific situation and your intended audience.