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1.
A Facetag is a Hashtag used on Facebook, but it does not do anything because Facebook is not Twitter.
"Facebook post: If 2 people (male and female) create 2 children. They have effectively replaced themselves (birthrate is "2.1") #BadatMATH"

"Comment on post: Hey baby.. Hashtags on Facebook don't do anything!"

"Response: Hashtags are used on Twitter by twits. That was a Facetag"
by cheddarbob2u March 27, 2013
 
2.
The process of tagging someones picture on the networking site Facebook.
"Hey Kass don't forget to facetag those pics from last night"
by tbutterw November 18, 2007