Learn English – “I am not really liking it very much…” vs “I don’t really like it very much…”

Can

"Could" is the past tense of "can", so let's start with "can".

"Can" has a number of meanings (see M-W). It can indicate possibility:

Do you think he can still be alive?

It can also refer to ability:

He can lift 200 pounds.

Could Present

"Could" has similar meanings but the time frame it refers to can complicate things. If you are referring to possibility, that's the same in the present:

He could still be alive.

Using "could" for the present perhaps adds a nuance. "He can still be alive" is sort of a yes/no statement--either he is or he isn't. "He could still be alive" implies that his status depends on conditions.

If you are talking about present ability, "can" is definitive:

He can lift 200 pounds.

This means that he definitely is able to do it. "Could" is conditional; there's an "if" or a "when" or other conditional term that modifies or limits the statement of ability. For example:

He could lift 200 pounds if he recovers from his injury.

Take the example in the question:

...a few Air Force helicopters could [not] achieve much

Without the surrounding context, this might have potentially referred to the present or future. In that case, the meaning might be referring to either possibility or conditional ability, depending on the context.

Could Past

The potential meanings of "could" change when referring to the past. The action has already happened, so whatever possibilities there were have already played out; they are no longer possibilities but a specific reality.

He could lift 200 pounds.

This means he definitely was able to do it in the past.

Returning to the example in the question:

...a few Air Force helicopters could [not] achieve much

As a past reference, this refers to what actually happened. The helicopters did (or didn't) achieve much.

Could have

"Could have" (done something) is used for saying that something was possible in the past, even though it did not happen. (Macmillan} Example:

You could have been killed.

If it had actually happened, you would use did, were, or a similar "actually-happened-in-the-past" word. Could have refers to a prior possibility whose time has passed.

Since could have means that it did not, could not have might seem like a double negative (what, exactly, is being negated by the "not"?). Here's why that isn't the case. The "could" portion refers to what was possible (or an ability). The "have" portion refers to completed action (the perfect; see M-W). Modifying "could" with "have" is what says that the "could" did not happen.

So could not have still refers to something that did not happen, but the referred-to action was a "negative" possibility; i.e., lacked the ability to happen (and the "have" means sure enough, it did not).

The example in the question:

...a few Air Force helicopters could not have achieved much

This refers to something that did not happen and (or because) it lacked the ability.

Firstly, both sentences are a subjective opinion given by someone, and they have exactly the same meaning. However, the difference lies in the syntax.

She seems crazy

is considered a personal sentence. This means that it is the opinion of the speaker, and the speaker doesn't shy aware from admitting it.

However,

It seems like she is crazy

is an impersonal sentence (See here for more details and examples). This means that, although it is still the speaker's opinion, they are distancing themselves from it, by saying "It seems that" + their opinion. They are trying to make themselves sound more objective or neutral, even when giving an opinion, which is always subjective.