Difference between initializing a C-style string to NULL vs. the empty string

Question

Are these three equivalent:

char* p= NULL;
char* q = "";
char r[] = {'\0'};

I suspect the first one is different from the rest, but I'm not entirely sure.

Answer 1

^{I'm answering for C++ even though the OP has also tagged the question as C. These are two different languages. It's not a good idea to conflate them.}

This declaration:

char* q = "";

used a deprecated conversion in C++03, and became invalid in C++11. We're now at C++14.

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These two declarations:

char* p= NULL;
char r[] = {'\0'};

are fundamentally different. The first declares a pointer and sets it null. The second declares an array of one item, which item is set to null.

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Regarding

” Are these three equivalent

the answer is no, not at all: one is just invalid, one declares a pointer, one declares an array.

Answer 2

char* p = NULL;

This assigns NULL to the pointer p which means that p does not point to any valid memory address.

char* q = "";
char r[] = {'\0'};

These both create empty strings and are basically equivalent. q points to a valid memory address, unlike p in the previous example. r is an array with an empty string.