constexpr const vs constexpr variables?

It seems obvious that constexpr implies const and thus it is common to see:

constexpr int foo = 42; // no const here

However if you write:

constexpr char *const str = "foo";

Then GCC will spawn "warning: deprecated conversion from string constant to ‘char*’" if -Wwrite-string flag is passed.

Writing:

constexpr const char *const str = "foo";

solves the issue.

So are constexpr const and constexpr really the same?