Bütün- singular ( the whole)
Tüm- plural (all)
-Bütün karpuzu tek başına yedi.
(He ate the whole watermelon by himself.)
-Pazardaki tüm karpuzlar çürük.
(All the watermelons in the bazaar are rotten.)
However, we don't generally care about the difference and use them interchangeably. For example, there is a famous song "bütün kızlar toplandık"(we, the whole girls gathered) as if the girls who are gathered lack some part from their bodies. It should be "tüm kızlar toplandık" (we, all the girls gathered)
But again, don't think about it. 1/100 person knows that rule in Turkey :D