Republic of China (ROC) = Taiwan.
People's Republic of China = (mainland) China.
The top MC (maximum card) is official issue of Taiwan Post - very nice.
The other maximum card was created specially for me, at my specific request, by my good friend S. in Taiwan. Thank you! :)
She is one of the best philatelic partners/friends that I have on 6 continents (nobody yet at a research base in Antarctica - I'm working on it :) ).
Starting with the existing stamp, she found a great image online (even more matching than the official image), then she asked for permission to reproduce it.
I think those images were already released into public domain, but anyway.
Then she designed and ordered custom picture postcards.
Then she went to her post office and obtained clean local postmarks on such maximum cards. As a philatelic handback, she took them right back and sent me the whole batch in an envelope. One MC from each different design.
I love her custom MCs even more! Besides, there's only 1 MC made in each exact configuration - unless she liked them so much that she created more, for herself :D .