Both... babies don't have sadness about death and stuff... that develops as they grow and learn... there's a lot a baby doesn't understand but does when they are older and that can be associated with emotions... Basic emotions are probably innate but much is influenced by nurture.
I say in support of this cases where the child was not properly socialised.. like the poor young woman who had been left in a room by herself and had to stay seated on a potty... I very much doubt she had normal emotions... i think she would have learned long ago not to cry or feel sad as it didnt do any good... she probably had a very limited range of happy...
I say it too as when we look at people... they very much vary in how much emotion they feel about any one thing... we had to read two case studies about two troubled teens, both of whom said they wanted to die... some people in the group were visibly tearful and desperately sad for one or both of the teens... others were unaffected .... we definitely vary.... and there are some people who seem not to feel many or all emotions aren't there?