The poppy was a flower.
Opium was an extract from opium poppies. It was also known as papaver somniferum, which translated to "pipe of poppy". (TV: The Talons of Weng-Chiang)
After World War I, the poppy became a symbol of remembrance. At a British Remembrance Day ceremony in which Tim Latimer was honoured, Latimer himself as well as the Tenth Doctor, Martha Jones, the vicar and a number of other attendees all wore poppies as a mark of respect to those that had fallen. (TV: The Family of Blood) In Crook Marsham, a wreath of poppies was placed at the monument honouring those who had died in the war. (PROSE: Nightshade)