Hello Magali,

Messages are specifically internal and emails are exactly that, emails. 

If you were to go onto a contact record in the chatter you will see the two buttons, log note and send a message. Send message will send an email to the contact as well any followers of the contact document. This is represented by the little person at the top right of the chatter with the number. 

When you log a note this will just keep a note on the record of whatever you type in, this will be displayed in the chatter. This is good if you have had a call with a customer and just want to quickly log details about the call for all the users of the Odoo system to view. 

You may be seeing emails inside the messages menu because once you send an email from a record it gets created as chatter/note on that record. Thus meaning that it is created in messages as well as an email. 

I hope this helps.

Thanks,