ハイヤー　(Hired car service) is very similar to a limo/town car service in major US cities. Many people in Japan using uber black used hire before uber became available. You can just just call a hired service like Kokusai or MK. Most of the Uber black service is provided by these hired car companies who contract directly with Uber. Uber is just easier to use because it's quicker (no wait times on the phone), don't need to explain your pickup location, easier to handle payment, and you don't need to communicate as much with the driver about destination/route.

Some of these hired companies now have their own apps, which make them easier to use. Because of the issue with surge pricing, I've largely switched back to Kokusai for airport runs.