Yep, you're certainly 100% right that printing was developed in the vicinity of China and that it later spread westwards.
When I say that the printing press was invented in Germany, I'm referring to the mechanical press mechanism developed by Gutenberg he based the device on existing machinery that had already been developed for wine presses. In all truth, I'd have been more accurate to have said "the printing press
as we know it today comes from mid-15th Century Germany" while we can be pretty much certain that the Chinese invented print, I don't think they had press
machinery as such... as you say ink would be applied to the woodblock or clay surface and paper would be sandwiched between, transferring the ink. I don't think machinery in the form of a 'press' was involved I might be wrong though, as it's been a while since I had my typography and print lectures, and we tended to go down the pub afterwards so that wouldn't have helped my memory.
What Gutenberg did was combine the various techniques, refined the inks that were used, and used his training as a goldsmith to perfect the techniques required to cast reliable metal type. All of these together with his press led to printing becoming cheaper and faster. He certainly didn't invent printing though, nor did he invent moveable type (the latter in particular is often credited to him). What he did was to invent the printing press
as we know it today.