Solution 1:

Comes from "Telegram". The answer is on their About page:

When we were kids we loved playing around with cameras -- we loved how all the old Polaroid cameras marketed themselves as “instant” (something we take for granted today). We also felt that the snapshots people were taking were kind of like telegrams in that they got sent over the wire to others -- so we figured why not combine the two?

http://www.thefreedictionary.com/-gram