The difference between Conversation and Discourse

When used as nouns, conversation means interaction, whereas discourse means verbal exchange, conversation.

When used as verbs, conversation means to engage in conversation (with), whereas discourse means to engage in discussion or conversation.

check bellow for the other definitions of Conversation and Discourse

Conversation as a noun (obsolete):

Interaction; commerce or intercourse with other people; dealing with others.
Conversation as a noun (archaic):

Behaviour, the way one conducts oneself; a person's way of life.
Conversation as a noun (obsolete):

Sexual intercourse.
Conversation as a noun (obsolete):

Engagement with a specific subject, idea, field of study etc.; understanding, familiarity.
Conversation as a noun:

Expression and exchange of individual ideas through talking with other people; also, a set instance or occasion of such talking.

Examples:

"I had an interesting conversation with Nicolas yesterday about how much he's getting paid."
Conversation as a noun (fencing):

The back-and-forth play of the blades in a bout.
Conversation as a noun (computing):

The protocol-based interaction between systems processing a transaction.

Conversation as a verb (nonstandard, ambitransitive):

To engage in conversation (with).

Discourse as a noun (uncountable, archaic):

Verbal exchange, conversation.
Discourse as a noun (uncountable):

Expression in words, either speech or writing.
Discourse as a noun (countable):

A formal lengthy exposition of some subject, either spoken or written.

Examples:

"The preacher gave us a long discourse on duty."
Discourse as a noun (countable):

Any rational expression, reason.
Discourse as a noun (social sciences, countable):

An institutionalized way of thinking, a social boundary defining what can be said about a specific topic (after Michel Foucault).
Discourse as a noun (obsolete):

Dealing; transaction.

Discourse as a verb (intransitive):

To engage in discussion or conversation; to converse.
Discourse as a verb (intransitive):

To write or speak formally and at length.
Discourse as a verb (obsolete, transitive):

To debate.
Discourse as a verb:

To exercise reason; to employ the mind in judging and inferring; to reason.

Examples:

"rfquotek Dryden"
Discourse as a verb (obsolete, transitive):

To produce or emit (musical sounds).