My guess is the following: ASML produces the lithography machines, and TSMC/Samsung/<chipmaker> uses them in mass production. What I hear from the Dutch news is

My guess is the following: ASML produces the lithography machines, and TSMC/Samsung/<chipmaker> uses them in mass production. What I hear from the Dutch news is that the development process is very much a cooperation between different companies. What works in ASMLs lab will likely need a lot of tweaking before it can be used in mass production.