Re: What's the difference?
There is almost no strict distinction between the meanings of "dialogue" and "conversation".
However there seems to be an idiomatic tendency to suggest that:
(a) a dialogue is more centred upon one particular topic, while
(b) a conversation may more freely move generally from topic to topic.
In both cases it is presumed to be an oral (spoken) activity.
Reading has nothing to do with either.
Dialogue and conversation
The meaning of the word is in the context. Often when you read the word dialogue its in a more formal situation or refers to a specific situation, like a play or in an academic setting.
Conversation is more often used to communicate the idea of friends talking, or people debating in an informal setting.
You can have a conversation with yourself, but generally speaking the meaning of dialogue points to 2 or more people (monologue MONO is one person dialogue DIA is many or 2+).
Hope this helps.