> The chinese developed printing and movable type but not a "full press"? Not sure if I follow. I'd say the chinese/koreans invented the movable type ( metal type ) and the printing press but latin/alphabet languages/writings were better suited to being exploited to movable type/printing press than the chinese writing system? A movable type printing press based on 26 letter is far better than one based on thousands of characters. But it's still the printing press.
There's a lot to unpack here.
Printing, specifically, is a means of transferring ink to paper (or parchment, but paper tends to work better for printing for mechanical reasons). There are several different variations on the idea, but the original genesis of the idea and much of the early variation does originate in China.
The basics of printing boil down to: you have a raised platform that contains the thing being printed, you cover that with ink, you place the paper on top of it, and then you apply pressure to transfer ink to paper. For the Asian woodblock printing, I believe pressure was mostly applied via rubbing.
Movable type was an innovation that allowed you to build the block that was used for printing out of reusable components, which dramatically cuts down on the time it takes to prepare the blocks. East Asian languages are well-suited for movable type because their language is already written in a highly grid-based system; by contrast, the Latin alphabet has characters that bleed into other's boxes all over the place (kerning is a thing in Latin, not in Chinese). Extending printing to the Latin alphabet came with a lot more typographic changes than you'd think.
Gutenberg made, or at least synthesized for the first time in one piece, several innovations [1] in his press: the reuse of press technology to apply force evenly and quickly to paper; the development of a lead alloy for type that was long-lasting and could withstand the forces with less wear; the development of more uniform molds for the type; the development of better inks for pressing against the paper.
It's certainly true that the innovations of printing and movable type are Chinese. But those innovations, while necessary, were not sufficient to facilitate the massive spread of printing to make books cheap and ubiquitous. Extra innovations that Europeans did (in typecasting and the press itself, most notably) were also necessary.
[1] It's debated how many of these were actually done by Gutenberg himself versus how many were developed by other contemporary European shops and reused by Gutenberg. In either case, everything I'm listing was innovated in Europe, not in China.