You're right that pierogi, and in fact all dumplings, and even pasta, originate from China. However, they are different. The differences may be subtle to someone who is not familiar with them, enjoys generalizations, or lacks taste buds.

The world of dumplings literally spans the globe and is extremely varied!

You can put different things in them. Even if you look at "meat stuffed dumplings", you can use different types of meat, that is prepared and flavored in different ways. The dough can be made of different types of flour and with ingredients in different proportions. They can be boiled, deep fried, pan fried. They can be eaten by themselves, or doused in butter, fried onions, sour cream, bacon bits, or who knows what. The choice of stuffing is tremendous, spanning meat, cheese, potatoes, fruits, and mushrooms! Don't even get started on different shapes, which are also an important part of the meal.

It's like saying "bread is bread" and throwing croissants, sour rye, and cron-bread into the same proverbial basket. Technically true, but does not add much to the conversation.

European (and British) tea is just a version of Chinese tea, but differencies in tea culture are huge.