Learn English – Is it okay to say “15 minutes of four” in English

We can't assign a percentage of certainty to it, but it isn't close to 100%. Perhaps 60-85% certain is close to what it means for most native speakers. The more emphatic the statement (stress and pitch and volume are involved, because this is primarily spoken English, but in written English it might be underlined or in bold font or in capital letters for emphasis), the more certain the speaker/writer is. I'm quite sure probably means about 90-100% certain, however.

There are at least two ways these terms can be used:

1) They can be used to indicate assent:

For example:

We need some more eggs to make the soufflé. Can you go buy some?
Alright. (or, Okay.)

2) They can be used to indicate that the quality of something is "satisfactory but not exceptionally or especially good":

For example:

How was the movie last night?
It was okay. (or, It was alright)

In these two contexts, I find these terms pretty much interchangeable. In the first, you agree, but without any particular eagerness. In the second, they both convey about the same sense of enthusiasm (or apathy).

I will offer an opinion that differs slightly from Mowzer's: I think they are both somewhat general and informal terms. If for some reason more formality, politeness, or precision is called for, I would recommend using different words altogether. For example:

Judge: I'll need you to approach the bench and take the oath.
My response: Yes, your honor. (not, "Alright" or, "Okay")

English Professor: What did you think of the Faulkner story you read this weekend?
My response: It has a good message, but it's a little dry. (not, "It's alright" or, "It's okay")

Girlfriend's mother: We need some more eggs to make the soufflé. Can you go buy some?
My Response: I'd be glad to. (not, "Alright" or, "Okay")

I think your question is a fair one, and your analogy is a good one. But, in this case, I think the two words are much more interchangeable than, say, broke and bankrupt.