The name of an array usually evaluates to the address of the first element of the array, so array and &array have the same value (but different types, so array+1 and &array+1 will not be equal if the array is more than 1 element long).
There are two exceptions to this: when the array name is an operand of sizeof or unary & (address-of), the name refers to the array object itself. Thus sizeof array gives you the size in bytes of the entire array, not the size of a pointer.
For an array defined as T array[size], it will have type T *. When/if you increment it, you get to the next element in the array.
&array evaluates to the same address, but given the same definition, it creates a pointer of the type T(*)[size] — i.e., it’s a pointer to an array, not to a single element. If you increment this pointer, it’ll add the size of the entire array, not the size of a single element. For example, with code like this:
char array[16];
printf("%p\t%p", (void*)&array, (void*)(&array+1));
We can expect the second pointer to be 16 greater than the first (because it’s an array of 16 char’s). Since %p typically converts pointers in hexadecimal, it might look something like:
0x12341000 0x12341010