What's the difference between new char[10] and new char(10)

The first allocates an array of 10 char's. The second allocates one char initialized to 10.

Or:

The first should be replaced with std::vector<char>, the second should be placed into a smart pointer.

new char[10];

dynamically allocates a char[10] (array of char, length 10), with indeterminate values, while

new char(10);

again, dynamically allocates a single char, with an integer value of 10.

char *a = new char[10];
...
delete [] a;

The above dynamically allocates and deallocates 10 contiguous memory slots that can be used to store chars.

char *a = new char(10);
...
delete a;

The above dynamically allocates and deallocates one memory slot that is initialized with the integer value 10, equivalent to the char value '\n'.

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Do NOT use the std::vector<T> if you do not first understand pointers. Knowing how memory allocation and pointers work will make you a better programmer.