Your subject line & description are contradactory to each other. I am assuming you are looking difference between deactivate & delete.
Deactivate and delete are same from destination (publish) point of view (removes page/assets for crx). At source (Author) delete action removes the page/assets whereas deactivate marks page/assets as deactivate.
SOrry, my subject is wrong and thanks for the response. But when I use the replication agent to deactivate the page in a java program ( not via workflow nor from site admin) I dont see this behavior. I mean if I write a java class to use a replication agent and pass it a path (page or node) I see following behavior:
1. Page is NOT marked as deactivated on Author
2. The page/node is deleted on the destination.
What extactly marks page as deactivated on author instance.
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Using api directly should also update the status. The page you activated, verify if last replication action, replicatedby property exists & updated.