Are USB cables device-specific?

The U means universal indeed, but some manufacturers (such as Apple) choose to provide their own proprietary USB cables -- which are not interchangeable -- while others provide generic USB cables which are interchangeable.

All standard USB connectors by pinout.

In picture form: micro USB on the left, then mini USB, then regular full-size B and A USB.

The U in USB means Universal. They're totally interchangeable. I just keep one around and the rest as backups/to lend to others, it works pretty well.

They are interchangeable, but you will notice that they are not all same regarding build quality. I have a bunch of mini-USB cables, but only few of them can power a USB hard-drive without a secondary jack.

For devices not hungry for power, usually it does not matter.