AFAIK there is no equivalent to the Matlab builder (yet?). There are some similar functionalities but, as far as I understand and know, there is nothing that would perfectly match what you seem to need. For deploying functionality written in Mathematica for use from a C# program I see these three possibilities:
Deploy as Mathematica-Application (with GUI)
you can either deploy such programs as CDF-documents, which then can be run either with the CDF-Player or Wolfram Player Pro. You could also create a "normal" Mathematica application, which exclude the CDF-Player. Of course these will both also run with a full Mathematica. To run with the cost-free CDF-Player you'll usually need some extra effort and many realistic problems can't be solved within it as it for example can't import external data and has some other limitations. For Player Pro and CDF-Player the connectivity to your C# program would basically be limited to that you could start them from there, maybe passing some information to them via "tricks" like environment variables.
- Licensing: if you manage to supply the desired functionality as a free CDF-document no licenses are actually needed (but make sure to read the exact conditions). For Player Pro you have to buy licenses which have a reasonable pricing if you need only a couple of them, but if you need something like 1000 of them you'd have to contact WRI for a pricing (it is somewhat unclear whether they offer floating licenses for it or not). For a full Mathematica there are floating licenses, but of course these are quite expensive and only applicable if only a few of the 1000 computers will need your application at the same time.
- Deployment: you'll need to install a relatively large package (even the free CDF-Player basically is a full Mathematica without the documentation) on every computer to use this kind of application. This might or might not be a problem for you (or the responsible IT department).
Connect to Mathematica
For this to run you'd need a full Mathematica listening (neither CDF-Player nor Player Pro can be used like that). If you only need Kernel functionality, you could either connect to a local installed Kernel or have Mathematica installed only on a remote server and connect to that from your C# program, but you'll need special licensing for that (This is possible either by MathLink or e.g. web services, I'm not sure whether NETLink can connect to remote Kernels). For interactive plots -- which are front end functionality -- you'd need to have Mathematica installed and licensed on the target computer in any case. Of course you could instead write the interactivity within your application and only ask Mathematica to produce the graphics.
Compile Mathematica functions to Libraries via C
if the functionality you wrote can be compiled with
Compile, you could create C-functions/libraries/executable from it (see the CCodeGenerator tutorial). These can in combination with a minimal "WolframRTL" library be used from other programs without the necessity of anything else installed or licensed on the target computer. This is the approach that I think comes closest to what MATLAB builder(s) provide but is probably not that automated (yet), it's all included with a regular Mathematica though. The main drawback of this approach is that of course the functionality that can be compiled is quite limited and explicitly excludes everything that you have mentioned to be of interest to you (and most of why anyone else would want to call Mathematica functionality in general)...
Note that I'm not with WRI and the above information could not be entirely correct or up to date. I would also fully support Cuboids suggestion that you should contact WRI and explain them what you need, maybe they'll have or create a good solution for you...