Why
Because x++ expression first returns the value of x then it increments it, while ++x first increments it, then returns that incremented value.
Just for experimentation purposes, you can verify this by using the preincrement like this
// Don't do this, it's just to explain why it works.
addCount () {
this.setState({count: ++this.state.count})
}
Then it'll do what you want, however it's not idiotmatic, because it does mutate directly this.state.count.
Idiomatic way
In ReactJS you don't want to mutate this.state.count directly, so your first example is more idiomatic:
addCount () {
this.setState({count: this.state.count + 1})
}
References
MDN postfix/prefix increment operator ++