What is the difference between USB Mini A and Mini B?

USB specs defined two types of Devices at first. A devices, i.e. Hosts like your pc, and B Devices, i.e. Peripherals like a printer. At first, only standard size existed. Then mobile devices needing a smaller connecter, Mini-B was created. It is still for Peripherals only. Then OTG was added, creating the need for Mini-A (Miniature Host) and Mini-AB (Mixed, OTG device).

So Standard A Male to Mini B Male cables are for use from a Standard Host, to a Mini Peripheral. I.E. Your PC to a Cell phone.

Now, A Mini-A Male to Standard A FEMALE is allowed, as an adaptor, for OTG purposes. Mainly hooking up a standard device to a OTG host. Fairly common now. I have had tablets and phones that came with them in the box. A Mini-A Male to Standard A Male is non-standard as all heck.

The color of the connector on the cable is also defined within USB Specs.

Notably, USB Mini is depreciated and has been replaced by USB Micro for years now.

http://www.usb.org/developers/onthego/london/OTG_mechanical.pdf for an entire breakdown (simple to read) on the cable connector setup, as presented by the USB Implementers Forum.

The difference only matters for On-The-Go applications, i.e. special cases when a device such as a printer or cellphone is acting in a "host" role rather than its usual "peripheral" role. For your purpose, as long as the cable fits it will work and perform equally well to any other.