The two questions you link to are to do with different chargers, not the cables. If two cables both adhere to the USB standard, they're interchangeable. You can tell if a cable adheres to the standard, as it will have the USB logo on one or both of the plugs. It's not allowed to display the logo if it doesn't meet the spec. There are two cases where you might have a "USB cable" that really isn't (and thus doesn't have the logo):-
I've seen cheap cables that don't have the D+ and D- lines wired correctly. They ought to be a twisted pair, as USB uses differential signalling to make it more resistant to noise. But the cheapest cables save money by having a single line that's only wired to the D+ pin. These cables will be unreliable and might not work with some devices.
Some devices use a USB port to charge but not to transfer data (i.e. they're not USB devices). Examples include Bluetooth headsets and game controllers. These devices sometimes come with a cable that looks like a USB cable but only has the power pins wired: the data pins aren't connected to anything. Such a cable can only be used for charging.
Apart from these exceptions, the cable itself makes no difference (as long as it's not physically damaged). What makes a difference is the charger: the thing you plug the cable into, that also plugs into the mains. For faster charging from mains power, manufacturers get around the limit on how much voltage and current USB is specified for by introducing their own extra modifications to USB.
These allow the manufacturer's charger to charge compatible devices faster. However, so that the charger still meets the USB standard, and won't fry a standard USB device, it can only supply the extra voltage or current if it detects that the device is compatible, using extra pins, or by having the pins wired together in a special way. Devices that don't have the manufacturer's modification will only charge using standard USB current, so will charge more slowly.
Because there's been such a need for high-powered charging, recent revisions of the USB standard have added more support for chargers and have increased the current limit, but the manufacturers still use their own extensions (to make sure chargers from the same manufacturer are interchangeable).
