Matlab versus simulation products such as ANSYS an

This may be the wrong place to ask this, but I can't find a better place on the SE network. I've briefly worked with both Matlab and Ansys, and from what I have learnt/can gather, Matlab is a programming environment that has functions that perform common math, visualization and analysis operations. You primarily write programs in a textual fashion (.m files) or use Simulink to generate flow graphs (model-based development). Ansys on the other hand is primary a simulation environment where quite a lot can be done simply with the GUI (3D models, physics domains, configuration, display settings), and you can add equations at various points in the simulation engine in order to modify the simulation flow.

Whatever I understand is cursory and only serves as an overview. Can anyone give me a suitable real-world comparison between Matlab and Ansys (or any other simulation product such as COMSOL) that would allow us to understand when to use which, and the weaknesses of each system.

I haven't used Ansys, but Ansys is often compared with Comsol, and I've used Comsol and Matlab for years.

Matlab:

Programming language and environment that runs it. Which means it can do anything (that any other programming language can do). What are its highlights, compared to other languages?
- Hundreds of built-in functions to work with Matrices. For example, in one project I needed to do simple matrix algebra (add, multiply, scale matrices), and also needed singular value decomposition. SVD is not something you could write in 50 lines of code, so I needed a ready-made library. At the time I used a library for Java, and wrote my own code for representing matrices and doing matrix algebra on them. That's a few hundreds of lines of code. Had I used Matlab, it would have been about ten lines of code, because all of it is there. I would have needed only to type help svd to find out how to use it. However, if you don't need any of that, stay away from Matlab at all costs! There are much better languages that are free.
- Great to use as a calculator that is always open on the desktop, and can do back-of-the-envelope style calculations.
- Plotting graphs. Many academics recommend Matlab as the tool of choice for producing publication-quality graphics. These can be exported as PDF and imported into Inkscape for further editing. The best thing is that commands for plotting a graph could be put into a script file, and then parts of it can be changed later as needed, which can save a lot of work compared to manually drawing a graph (imagine you wanted to change the axes or symbols used to present the data points).
- Personally, I also use it for curve-fitting. It has many toolboxes, one of which is a neat tool that allows me to find equations that model a set of data points.

Comsol:

Specialised tool for solving partial differential equations (PDEs) on complicated domains using the finite element method (FEM). This might sound obscure, but many real-world engineering needs reduce to this. Such things as:
1. Finding loads, stresses and strains in civil engineering structures with complicated real-world geometry (what happens when there is gusty wind blowing onto a building or bridge?)
2. How do currents flow in particular conductive objects?
3. Chemical reactions in various industrial reactors.
4. What is the power efficiency of a generator (magnet spinning in coil) design?
5. How to place aircon outlets in a nontrivially-shaped room to achieve both good temperature distribution and good efficiency?
6. Comsol, as any other FEM tool that can work with arbitrary equations, can do multiphysics, which means, for example, that one could solve for chemistry of a battery, as well as the temperature and pressure, and how that feeds back into the chemical reaction (speeds up or slows down). Compared with a tool where you need to provide the equations, in Comsol, most of the things that would be needed to solve most problems are already there, and just need to be selected and applied to the geometry, which is also built inside Comsol. Also, equations of arbitrary description can be introduced.
The physical descriptions of how these physical substances behave are called PDEs.
Once Comsol has finished solving a problem, the data could be exported for post-processing into Matlab, which has much more versatile tools for manipulating data and making various plots.