They are talking as if language was some platonic construct like a Turing machine with an infinite tape and you are talking about the concrete reality where there are no such things as an infinite tape.
Both viewpoints are useful, they can prove general properties that hold for arbitrary long sequence of words and you put a practical bound on that length.
Both viewpoints are useful, they can prove general properties that hold for arbitrary long sequence of words and you put a practical bound on that length.