The difference is externally powered hubs can provide a full 500mA on each port on the hub. Bus powered hubs can only draw 500mA from the host controller(upstream) so for example with a 4 port hub can only allocate 100mA to each port (the remaining 100mA is used my the hub itself). A lot of USB devices require a full 500mA (called high current devices) such as wifi adapters or USB bus powered hard drives. If you plug a USB device that requires high current it will either: 1) not work at all 2) it will work interminably 3) act like it's working but not really work or 4) the operating system will shutdown the device give you a current overload error.
#4 is what *should* happen 100% of the time per the USB spec, but in reality there are a lot of non-compliant USB devices out in the marketplace.
I've never heard of any damage with caused by connecting high current devices to bus powered hubs, I think that's because the USB controllers are smart enought to shut themselves down if they get overloaded.
Hope that helps.