No. The skull and crossbone was just one flag that came about due to popular culture which said a pirate had to have a parrot, peg leg and a skull and crossbone flag.

Pirates carried different flags that had different meanings i.e. a skull and crossbone or something similar meant that it was a pirate ship (used to intimidate vessels so they wouldnt have to fight), red meant that no quarter would be given unless the crew surrendered quickly.

Information is extremely easy to come across on the topic on the internet and funny enough Assassins Creed 4 details some pirate flag information.

http://www.elizabethan-era.org.uk/pirate-flags.htm

https://en.wikipedia.org/wiki/Jolly_Roger

http://www.sea-thieves.com/education_pages/seathieves_edu_flags.htm