Difference between (function designator) and {function pointer}? - c

Question

In clang, a pointer to a function and the designation/designator have distinct resulting grouping symbols, parenthesis compared to curly braces as seen in the code fragments further down.
What is:
type * type(*)(type)
used for and versus/what is:
type *(type)
used for? Curly braces are for use in lists, compound statements and aggregates while parenthesis are primarily used for ordering, grouping, casting and arguments.
It looks like the first is a type reference to a function pointer accepting a specific type argument which, if enclosed in parenthesis either orders the group be evaluated individually if part of a larger expression or creates a cast which after the resolution of the function would convert it to a specific value of the return type of the specified size and alignment requirements instead of the binary sequence containing the value.
The second one is in a block with curly braces and thus a compound object or statement block since I can't see how it would be attached to an aggregate though it may be reference to a function body result of a call.
The second snippet looks like a type reference to a type defined or object group and, since a type may not share a name with an object, effectively making it a keyword, I presume that this somehow creates a named object that is multiplied with itself, or is a reverse cast or something since keywords with an asterisk have no real use aside from object declarations.
P
Why does the initial have parenthesis enclosing the symbol whereas the second symbol uses curly braces?
For example, the following code fragment when compiled,
.
(*function)(1);
mentions the symbol in the comments after compiling is noted as:
(type *(*)(type))
with parenthesis encompassing the representation in the compilation log of the console.
.
whereas:
.
function(1);
mentions the symbol in the comments after compiling is noted as:
{type *(type)}
with curly braces encompassing the representation in the compilation log of the console.
.
What is the distinction between the two for, and under what circumstances is it practically applied in any usual/useful contexts?
My general observations of the syntax and semantics of the C language suggest to me the first appears to be a basic ordered-group expression which may be used in a comma-separated list or as a function parameter whereas the second appears to be a struct, union or block statement.
I was exploring function pointers and so I tried both and those two notes were clang's comments of the compilation. None of the other 5 posts I read seemed to clarify the nature of the grouping symbols in any context but did provided additional insight to function pointers and their applications.
Thank you!

Answer 1

function designator is an expression with function type.
for example in
a = foo(x);
foo is a function designator.
Function pointer is a reference to the function. Function designators decay to function pointers when used as values.
int (*fptr)(int) = foo;