const vs constexpr on variables

No difference here, but it matters when you have a type that has a constructor.

struct S {
    constexpr S(int);

const S s0(0);
constexpr S s1(1);

s0 is a constant, but it does not promise to be initialized at compile-time. s1 is marked constexpr, so it is a constant and, because S's constructor is also marked constexpr, it will be initialized at compile-time.

Mostly this matters when initialization at runtime would be time-consuming and you want to push that work off onto the compiler, where it's also time-consuming, but doesn't slow down execution time of the compiled program

constexpr indicates a value that's constant and known during compilation.
const indicates a value that's only constant; it's not compulsory to know during compilation.

int sz;
constexpr auto arraySize1 = sz;    // error! sz's value unknown at compilation
std::array<int, sz> data1;         // error! same problem

constexpr auto arraySize2 = 10;    // fine, 10 is a compile-time constant
std::array<int, arraySize2> data2; // fine, arraySize2 is constexpr

Note that const doesn’t offer the same guarantee as constexpr, because const objects need not be initialized with values known during compilation.

int sz;
const auto arraySize = sz;       // fine, arraySize is const copy of sz
std::array<int, arraySize> data; // error! arraySize's value unknown at compilation

All constexpr objects are const, but not all const objects are constexpr.

If you want compilers to guarantee that a variable has a value that can be used in contexts requiring compile-time constants, the tool to reach for is constexpr, not const.

I believe there is a difference. Let's rename them so that we can talk about them more easily:

const     double PI1 = 3.141592653589793;
constexpr double PI2 = 3.141592653589793;

Both PI1 and PI2 are constant, meaning you can not modify them. However only PI2 is a compile-time constant. It shall be initialized at compile time. PI1 may be initialized at compile time or run time. Furthermore, only PI2 can be used in a context that requires a compile-time constant. For example:

constexpr double PI3 = PI1;  // error


constexpr double PI3 = PI2;  // ok


static_assert(PI1 == 3.141592653589793, "");  // error


static_assert(PI2 == 3.141592653589793, "");  // ok

As to which you should use? Use whichever meets your needs. Do you want to ensure that you have a compile time constant that can be used in contexts where a compile-time constant is required? Do you want to be able to initialize it with a computation done at run time? Etc.