Though very similar, an "aim" is a general direction or intent, while an "objective" is a more specific or concrete goal or accomplishment. A business may aim to get bigger yet have an objective to increase its market share by 5 percent within 12 months.
An aim is something a person or business wants to do; it's a statement of direction that drives certain activities. An objective is the end target. A person or company can also measure performance against an objective by evaluating whether the specific target was reached in the time allowed. A sales rep may aim to sell more next month, but a goal allows for a measurement to gauge success at the end.