The differences do matter.
The Uno has a chip on the board to convert USB to serial.
The Micro has this on the chip itself.
But it also has a ICSP connector.
You can use that to upload to the Micro, and the Uno can do that for you.
Uploading using the ICSP connection might end up in loosing the bootloader in that micro.
But that’s already quite useless to you at the moment if i understood you right.
There’s also RX and TX on the Micro.
These could be used to upload to the Micro, using the on board USB adapter.
For that you need to keep the reset line on the Uno LOW, so the 328 stays inactive.
You need to manually reset the Micro when the upload starts.
That is time critical and therefore will generate some trouble to get the upload going, you’ll have to try multiple times.
Are you sure it isn’t just a question of installing the correct drivers for the Mirco (be sure you have Administrator rights when you do that) ?