First let me correct your "weather" to "whether". Then let me say that whether is correct here, and if is not. If addresses one condition that is either true or false; whether addresses two conditions, one of which is true and the other false. Therefore you are correct that if implies a conditional situation and whether does not—the existence of two conditions is unconditional.
That said, the first sentence is not conditional and the second one is; that's the difference. To clarify this, let's rephrase them a bit more formally:
I wasn't able to tell whether he was annoyed or tired.
I wouldn't have been able to tell whether he was annoyed or tired.
The first sentence says you tried to tell and couldn't, the second says that you expected that if you tried to tell you wouldn't be able to.
Short answer: Yes
The difference is that the past tense means the action happened at some specific time in the past, and the present perfect means the action happened at an unstated time during a certain time interval that started in the past and continued to the present—maybe more than once during that time interval, depending on what you're talking about.
This action occupied the entire time interval from 1997 until now, and will probably continue:
Brenda has worked at Merriam-Webster since 1997.
This action occurred sometime during the speaker's life so far, perhaps many years ago, perhaps recently, perhaps more than once:
I have seen war.
This action occurred at the very end of the time interval (the time interval is that of the whole race):
Jones has won the race!
Long answer: No
The reason this topic is hopelessly complicated is because reality provides an infinity of different situations, and what time interval is reasonable to talk about varies for each situation.
For example, the time interval for the following question starts at roughly 11:00 a.m. this morning:
Have you eaten lunch?
The question literally means, "During the part that has elapsed so far today of the daily time interval when people normally eat lunch, did you eat lunch?" If you already ate lunch, then you probably don't want to go to lunch now; if you did not already eat lunch, then you might be interested in going to lunch with the speaker now. A person wouldn't ask that question after the middle of the afternoon, because that would be too much later than the normal time to eat lunch. The question leads you to think of the time period for lunch as a sort of window of opportunity that is still open, and asks whether that opportunity has already been exercised.
There's another source of endless complexity: the fact that you are referring to a time interval influences the way a listener understands the verb after have as well as the other words in the sentence.
For example, this sentence means that Chris performed the duty of phone-answerer last week, and answered the phone many times:
During the past week, Chris has answered the phone.
Using the perfect tense suggests that you might mean that the action fills the entire time interval, so the above sentence leads a listener to understand answering as performing a week-long duty to answer the phone whenever it rings. (This would probably be at a business.) Also, it would be strange to speak of a single instance of answering the phone in the present perfect if it happened at some unspecified time during the past week. If Chris answered the phone four days ago, the phone call is surely over by now.
The next sentence probably means that Chris answered the phone once. But it could also mean the same as the previous sentence:
During the past week, Chris answered the phone.
The reason it could mean the same as the previous sentence is the time interval is explicitly spelled out, and answering can still be understood as performing phone-answering duty, regardless of the tense. The past tense doesn't suggest that the action filled the time interval, so it doesn't suggest the “week-long duty” interpretation as strongly as the present perfect. But the past tense doesn't contradict that interpretation, either.
I spoke.
I have spoken.
The first of the above sentences just means that you said something. The second one means that you have said everything you have to say, and probably that you don't want to listen to or address any objections. Because the present perfect suggests a time interval that ends at the present moment, it can suggest that an action filling that time interval is now complete and will not continue. Obviously, though, that's not the intended meaning of the earlier example of someone working at Merriam-Webster since 1997.
Here's an example that follows the basic principle plainly, but is still subtle:
I wrote two novels in 2009.
I have written two novels. [The time interval is the speaker's whole life so far.]
I have written two novels in 2009. [Ungrammatical, because 2009 is over. But this would be grammatical if said during 2009.]
I have written two novels this year. [This is OK, because this year is still present.]
Yet another use of the present perfect is to establish the time frame for a news story. “Until now, most efforts to capture carbon have been expensive, in dollars and in energy.” The past tense (“were expensive”) would mean the same thing, but the present perfect suggests that the rest of the story will describe how that technology is now changing. It leads the reader to expect that the time period covered by the story will be very broad, on the order of years. Beginning a news story in the past tense suggests a very short time frame.
You just have to learn through experience to understand why people sometimes want to refer to a time interval rather than just the specific event. And you learn to infer what that time interval is, since it's usually implicit. Eventually it becomes effortless, but no simple rule could ever cover all situations.
Best Answer
In this case there is no difference.
Usually, the difference would be one of timing:
I eat breakfast
vs.
I am eating breakfast
The former would be for a regular activity, the latter for what I am doing right now.
But when it is a large group of people, the two meanings merge somewhat; someone, somewhere, is using a cheque right now.