Mathematica is a real mathematical software, or rather, a "calculation software", which is used to calculate things. For example, calculate the factorial of 100, such as the root of a polynomial, such as drawing the shape of a curve. It can do these things well, but it is only limited to this. It is almost impossible to develop new algorithms with it. Therefore, no one uses mathematica in real mathematical research or research in related fields, just as mathematicians don't really need to use calculators.
Mathcad is actually not a math software, but a "writing math" software, which can be easily input, but its advantages are limited to this.