I want to connect my Arduino Nano to PC via USB cable. It is described that it needs USB Mini-B connector. But all Mini-B cables are out of stock and only USB Mini-A are available. Will it work with Mini-A. Because I did not find any differences between those two types in terms of connector shape.
No Mini-A will not work.
Type-A connectors are for upstream connections (PC) and Type-B for downstream peripherals (Arduino)
Mini-A was a thing in early 2000s for USB-OTG applications but dropped out of the standard in 2007.
Also they have a different shape. Otherwise a different name wouldn't make much sense.
I don't know where you live but unless it's the Mount Everest it is rather impossible that you cannot get a A-Mini-B cable. Just pick another vendor.