Difference between Publish / Activate / Replicate ?

• Publish a page 
• Activate a page
• Replicate a page to publish .

Actually these three terms means same thing which is pushing data to publish instance or making a page available in author  to publish instance.

• Publish / Unpublish
  These are general terms used by everybody to make your content in author to be publicly available in publish environment. 

• Activate / Deactivate
  These terms are synonymous with publish/unpublish and meaning is same as Publish / Unpublish. They are more common in the classic UI and can be accessed from siteadmin or sidekick commonly. 
• Replicate / Replication
  These are the technical terms used to indicate the movement of data (e.g. page content, files, code, user comments) from one environment to another; i.e. when publishing, or reverse-replicating user comments.