When is it necessary to define a function in "syms"?

What is the difference between the following two codes? They both work. When is it necessary to define a function in "syms"?

syms f(x)
f(x)=x^2
f(2)

syms x
f(x)=x^2
f(2)

Answer 1

[Walter Roberson]

It is necessary to define a function in syms when you are creating a symbol to designate an unknown function. For example,

syms f(x)
dsolve( diff(f,x) == cos(x) )

It is not possible to create an indefinite function using symfun() or assignment to f(x), or using feval(symengine) or evalin(symengine) or str2sym(). However it is possible to use

g = symfun(str2sym('g(x)'),x)
h(x) = str2sym('h(x)')

Only syms() and symfun() and assignment to something indexed at a sym have the logic to "bless" a symbolic variable into being of the correct class.