'Pan out' is neutral and could mean any result, good or bad. 'Pay off' is positive and refers to some reward for some effort or something risked, financial or emotional. "We're going to have to wait to leave until we see how the situation pans out." "His efforts with Julie paid off when she consented to go with him on a date." By the way, the term 'pan out' comes from gold prospectors trying to find gold by putting gravel in a pan with water and moving the pan back and forth. Gold was heavier and would stay in the pan - it would 'pan out'.

Pan out applies to any situation working out in the end. "Hopefully after all this trouble, everything will pan out" Pay off can be financial or not. In either case, the end result will make everything worth the time, effort, etc. invested (financial or otherwise). "All you sacrifice will pay off when your son becomes a doctor." This can mean your efforts were worthwhile, or she will benefit financially.