One of the real powers of humanist morality, or consequentialist morality in general, is that it looks to improve the world we live in. When we look at utilitarianism, then the idea of the greatest pleasure for the greatest number of people (or lack of pain) is tangibly about improving the world around us. Any other consequentialist moral value systems will broadly do the same. There is no notion of appealing to an afterlife or some realm that we are simply unsure of and have never experienced. It is all about the here and now.
As the Routledge Encyclopedia of Philosophy states:
Consequentialism builds on what may seem to be the merest truism, namely that morality is concerned with making the world a better place for all. Consequentialist considerations certainly figure importantly in issues of public policy. Penal, economic or educational programmes are standardly judged by the goodness or badness of their results.
All moral theories offer an account both of the right and of the good. They all tell us, that is, both what makes an action right or wrong, and what kinds of thing are good or valuable. It is characteristic of consequentialist theories to assess whether an action is right in terms of the amount of good it produces (see §4). Deontological ethical theories, by contrast, hold that the right is independent of the good: certain kinds of action are wrong, and others right, independently of the goodness or badness of their consequences (see Deontological ethics; Right and good).
On the other hand, theistic morality is a promissory note at best and seems to be a self-serving moral value system that has more to do with the afterlife than the world of the here and now. Even if the theist is being a good steward of the world and trying to improve it in some tangible way, the question should always be “why?” And when one pursues the questioning all the way down, the theist will find it gets to some axiomatic answer like “to get into heaven or avoid hell”. Even “to enter into a loving relationship with God” demands a further “why”, and the answer is certain to appear self-serving.
It is in answering the “why” questions that we see the difference between the two positions.