What is the moral difference between abortion and infanticide?

Many people accept abortion on the grounds that foetuses aren't persons, and that personhood is what defines the right to life. I've always been intrigued about what defines personhood; obviously attributes like consciousness (or the ability to suffer) and personal identity seem to play a role. Some would say you can abort a foetus because it has no sense of personal identity, it can feel no pain and its death will have a net positive effect. But could you not make this argument for a toddler? A toddler has hardly any rational faculties, it certainly has no developed sense of identity, and if you had a method of killing it painlessly, what would be wrong with that (say, if the toddler was draining an already financially struggling and drug addicted single mother)? Obviously the thought of this seems reprehensible, but where is the philosophical line here?