A product identifier is a string used to uniquely identify every publication you wish to sell from your app. The App Store/Google Paly uses it to retrieve information about a publication. So you need to create product id only when you want to sell your publication. You have to create one product id for each publication you want to sell.
You have to separately create product id on iTunes Connect and Google Play if you want to sell your publication on both AppStore and Google Play. Please be sure to use the same string identifier on both iTunes Connect and Google Play.