Detecting space-filling $D$-Branes in string theory I am currently studying Zweibach's "A First Course in String Theory" CH:9 and I have managed to understand mode expansion in the light-cone gauge, at the classical level. Right before deriving the explicit solution of the wave equation for the open string, he remarks "We will assume that we have a space-filling $D$-Brane".
In the classical sense, $D$-Branes are just hyper-surfaces that imbose Dirichlet boundary conditions at the ends of open strings. So in that sense, the existence of a space-filling $D$-Brane is equivalent to having no $D$-Branes at all. But in that case, how can we dynamically reason the existence or the significance of space-filling $D$-Branes. How does the picture change when we quantize the open string? Do we quantize the $D$-Brane, and if yes, how so? In the theory of quantized open strings, what additional features other than Dirichlet boundary conditions do space-filling $D$-Branes have?
 A: A space-filling brane has three effects:

*

*It carries a tension, thus it contributes to the overall energy of your setup, which is especially important for phenomenological applications.


*The brane allows open strings to end on it. An open string needs a brane to end on. Thus if you would have no brane you would also have no open strings ( actually they are equivalent, you can use either open strings ending on the brane or the D-brane itself to describe the same degrees of freedom)


*It contributes to certain RR-tadpoles. Again mostly important for construction phenomenological setups.
In general D-branes are dynamical objects, which can even be created and annihilated dynamically. The definition in terms of boundary conditions is just to get some intuition, but a brane is much more.
A: Initially, D-branes were just the shape of the dimensions in which a string obeys Neumann boundary conditions. Before the series of realizations now called the "second superstring revolution" and in particular Polchinski's "Dirichlet Branes and Ramond-Ramond Charges", "space-filling D-brane" would have been just another way to say "the string obeys Neumann boundary conditions in all spatial dimensions", and in some ways, it still is. But Polchinski realized that under T-duality between type I and type II string theory, the D-branes need to be charged objects under the Ramond-Ramond fields of type II supergravity.
Polchinski even discusses the 9-brane - the space-filling brane - explicitly in his seminal paper:

It [the 10-form of type II string theory] couples to a 9-brane, but what is that?  A 9-brane fills space, so the open string endpoints are allowed to go anywhere: This is simply a Neumann boundary condition. If there are $n$ 9-branes (which must of course lie on top of one another), the endpoints have a discrete quantum number: This is the Chan-Paton degree of freedom.

So in the type II view, the D-branes are charged objects under the Ramond-Ramond gauge fields, and their number produces Chan-Paton gauge groups in the effective theory. The existence of a charge is obviously different from the existence of no charge.
Your question of what distinguishes a D-brane that is everywhere from no D-brane at all is philosophically very similar to the question of what distinguishes a single D-brane from a stack of coincident D-branes, to which the answer also is essentially "the Chan-Paton factors", on which I've previously written here.
