What is the difference between aims and objectives in a research proposal?

This shows up generally in the English language, I've seen the exact same discussion in writing constitutions for not for profits, and similar answer applies.

Consider the context of a military plan:

• Aim: Secure the northern boarder.
• Objective: Increase garrison strength to 150 men
• Objective: Assassinate the neighboring warlord: McBaddie
• Objective: Rebuild border wall

Your aim is "What do we overall want" -- the what, your objective is "What will do to achieve it" -- the how. Once all your objectives are complete, then you should have thus completed the aim. Objectives are also "whats" and so can be the "aims" for subobjectives. Eg

• Objective: Increase garrison strength to 150 men
• SubObjective: increase recuiting in cities X,Y,Z
• SubObjective: Decrease training times of recuits by increasing hours of training per day by 25%.

So for a research proposal: say you are in the area of Sports science/mechanical engineering, working on bicycle design.

• Aim: to produce the most efficient bycycle in terms of cadence to power ratio.
• Objective: Develop a sensor accurately measure power that can fit into a pedal casing
• Objective: Determine normal cadence rate for cyclists, and the level they can be trained to vary it.
• Objective: Determine the most effective material to build gear systems out of.

There is no simple answer. From what I can tell, these terms were developed by bean counters with the typical description being that the aims are the what and the objectives are the how. The bean counters then talk about smart objectives that are specific, measurable, achievable, relevant, and time bound.

The quote I like best is from NIH NIAID:

start thinking about your planned experiments by first drafting objectives, known in NIH lingo as Specific Aims.

I think this circularity arises from the fact that NIH grants typically only have a specific aims section and does not have an objective section. The NIH says the specific aims

Includes the specific objectives of the research proposed (e.g., to test a stated hypothesis, create a novel design, solve a specific problem, challenge an existing paradigm or clinical practice, address a critical barrier to progress in the field, or develop new technology).

I hae always thought the description of the specific objectives sound like aims to me since I feel like they describe what is going to be done (test a stated hypothesis) and not how it is going to be done.

The key thing, regardless of the terminology is that grant reviewers nowadays want to know both what you are going to do and how you are going to go about it.