Subjective morality is probably synonymous with personal preference. You have already indicated that this is what you confuse with morality without god. You are wrong in this conclusion. It is a common canard of christians to present a false dichotomy between morality based on god or everybody choosing whether or not to eat babies.
Objective morality is the task of making moral judgements on the basis of a standard we can agree on with others. I have summarised this foundation as the 'flourishing of conscious creatures'. We know the basic needs of other humans since we all share the same physiology. It is always harmful to another person to kidnap and rape them. On this basis we can say that it is OBJECTIVELY wrong to do these things. It does not matter if somebody else does not share this view. They are wrong, objectively wrong.
John Rawls suggests a 'veil of ignorance' as a useful thought experiment in thinking about morality. Imagine yourself in an original position behind a veil of ignorance. Behind this veil, you know nothing of yourself and your natural abilities, or your position in society. You know nothing of your sex, race, nationality, or individual tastes. Behind such a veil of ignorance all individuals are simply specified as rational, free, and morally equal beings. From this position we can begin to think objectively about right and wrong. It is a more sophisticated version of 'do unto others' which predates Jesus of Nazareth by many centuries.
Absolute morality is a term favoured by theists and constantly confused with objective morality. It is synonymous with morality with divine fiat. Those things are good which god says are good and vice-versa.
But how do we know what god says? We have an ancient book but it prescribes moral standards of Iron Age goat herders. Sometimes it advocates love and at other times it positively approves of slavery, kidnap, rape and infanticide. It recommends behaviour that we all find repulsive. Should we follow our conscience or the revealed word of god?
God is a hindrance to objective morality.