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.
The main difference in meaning between imply and insinuate is this taken from Merriam-Webster on the term insinuate:
"The word insinuate, on the other hand, usually includes a sense that the idea being conveyed is unpleasant, or that it is being passed along in a sly or underhanded way ("She insinuated that I cheated")".
But another difference is this: A person who hears someone says something can have the impression the speaker is insinuating or implying this or that. That's fine. But the term imply or implication may also be used in formal logic and philosophy whereas the term insinuate itself is not a formal term.
A logical implication or material implication is formal term in logic. It is written like this: A implies B, where the word implies is an arrow that cannot be transcribed here. But you can view it here: logical implication and this is the symbol for implication or implies: ⇒
As for "insinuating desires" into technology, that is a metaphorical use of the term and suggests slying introducing them into technology, as opposed to just doing it outright or in a clearly visible manner.
Best Answer
First off, I wouldn't lose any sleep over it. I imagine you could swap the two in almost any context and I doubt anyone (regardless of origin) would notice.
That said, for all meanings not concerning computers, "disc" is probably more common in British English, and "disk" in American English (that's the OED's take, and matches my experience), but use whichever you prefer. You might think disc would be older, since the word derives from the Latin discus, but there are some pretty old "disk" quotes listed in the OED (one from the Philosophical Transactions of the Royal Society of London, 1665--so no American influence there).
For computers, I have to concede that the Apple page does have a point (though calling it a "distinct difference" is carrying it way too far towards prescription on what's clearly a descriptive issue--for that matter, so is devoting a support page to it). One pretty much always sees "compact disc". "Floppy disks" (for those that remember them) were sometimes called "diskettes"; which term came first, I don't know, but the association between the two probably caused the K spelling to stick. Personally, I would also spell "hard disk" with a K as well--since the term originated by analogy to "floppy disk", that makes sense. I don't think the optical/magnetic split between disc/disk is based on anything like logic, but it does seem to be the way things have developed (mostly: I'd still call a CD drive a disk drive). The OED even acknowledges this: "Some writers have used the spelling disk for magnetic ones (‘hard disk’, ‘floppy disk’), and disc for optical ones (‘compact disc’, ‘laser disc’).". But then, it also lists "compact disc (also disk)".
There might be some technical applications where one is used over the other, but it'll never be based on any logic, since the two words mean exactly the same thing, so if you run into that, just look around to see which is more common. ("Disc" brakes gets the wikipedia entry, but no one would wonder for a second what "disk brakes" were.)
As to why both exist: who knows? Both spellings have been around a long time, so it is surprising neither has died out (since there never seems to have been a difference in meaning between them, at least until Apple got involved). If I were to engage in rank speculation, I would wonder if "disc" didn't come into the language directly from Latin, while "disk" meandered in via the French disque.