MATLAB Compiler enables you to share your MATLAB programs as standalone executables (.exe) that run against a MATLAB Runtime. It supports most of the features in MATLAB, including graphics, and protects your intellectual property by encrypting your MATLAB code.
MATLAB Compiler SDK extends MATLAB Compiler by the ability to provide shared libraries (.dll, .so), so that your MATLAB programs can be packaged into software components for integration with other programming languages.
MATLAB Coder on the other hand, provides readable and portable C source code. It supports a subset of the MATLAB Language focused on algorithms performing numerical computations.
The high-level differences between the two approaches are summarized below:
You would use MATLAB Compiler to produce executables that can plot, and that can run on computers without MATLAB. The executable would, though, need to be run on the same class of operating system (Windows, Mac, Linux) as MATLAB Compiler was run on.
MATLAB Compiler SDK does not produce executables itself: it produces DLLs that you can call from other languages. What is produced can plot. The DLL would, though, need to be used with the same class of operating system as MATLAB Compiler SDK was run on.
Neither R2014a nor R2014b support using Visual Studio 2019. The newest Visual Studio that either one supported was VS 2013 Professional ( not Community or Express !! )
mex -setup has a limited list of compilers to search for, and it searches for exact versions. It does not look for "the most recent Visual Studios", it looks for those specific Visual Studios.
Over the years, the directory structure of the Visual Studios implementations has changed, so you have to know which version you are working with in order to set up the file names properly.