Gerundial and infinitival uses with 'aim'!

I happened to speak: Most policies framed by the government aim at improving the general welfare of people. Now this policy, adopted as a long term measure, aims to train the people, by and by, towards a digital economy.

One of my friends who listened to the talk asked me privately: Why did you use both a gerund and an infinitive after the verb ‘aim’? I answered: In the first sentence I was referring to the general policies while in the second I was referring to a particular one which we know.

Now, forum members, do you agree with me? If not, please explain why. I’d like comments from non native as well as native users of English.

I would suggest - ‘aim at’ + gerund suggests very much the idea of targeting as in - The Government is aiming at reducing the number of cycle road deaths by introducing more cycle lanes. This obviously is a continuation of the idea of shooting at a target as in - The gunman aimed his gun at the police officer.

‘Aim to’ +infinitive conveys more the idea of intention as in - The management at this hotel aim to please their clients in every possible way.

Is it that the gerund suggests a future (time-consuming) goal and the infinitive an immediate goal? I admit that this aspect of grammar, for me, is a hard nut to crack.

I think that ‘aim at’ with the gerund is mostly linked with its actual meaning rather than its grammatical function.

The grammar teacher wrote down the words with mistakes from her essay. Checking the essay she aims at correcting mistakes. (She knows that mistakes exist, and her target to correct them.)
She is checking every essay to correct the mistakes. ( I mean intention, so I can use infinitive. I dont know if there are any mistakes or not.)

Is this right?

Alan, as I rely on your concept of ‘target’ and ‘intention’ and look back at my own sentences, I find them to be conveying my idea correctly. So, would you support this contention?

I may offer my view thus:

The teacher checks all the essays usually because she aims at correcting mistakes. (target)

The teacher may not check all the essays now because she does not aim to correct each one of them. (intention)

This was the sentence which, if my memory serves me right, our teacher wrote on the blackboard to explain the difference in the 1950s. Any comments?