Can or could; modal verbs

These are not just any sentences with can or could. These are requests, and as such they have special usages.

There is a grammatical construction for telling people what you want them to do:

• Help me with this.

But instead of using the imperative, the speaker has asked a question. Using a question form is already indirect. The speaker is not asking for information. The speaker is asking for service, but indirectly, preserving the addressee's face by not imposing a demand.

Similarly, the use of modals is more softening. The speaker does not ask for a prediction or promise:

• Are you going to help me?

but rather merely a question about possibility -- can you? could you? might you be able to? do you think it's conceivable that you would? -- these are all standard phrases by now, though the long ones are for more formal occasions.

So it's not a matter of the two modals having different senses -- and, incidentally, there's no issue of doubt involved; it's all just politeness formulas -- but rather that modals are very complex and have many social and idiomatic usages that don't follow normal kinds of rules. In fact, every modal I know anything about is terribly irregular in just about every conceivable way. That's just the way they are.