Q:

Difference between make_pair and curly brackets { } for assigning a pair in C++?

I didn't find anyone answering this, is there any difference between the following : 
v.push_back({x, y});

and : 
v.push_back(make_pair(x, y));

Assuming that v was declared this way :
vector<pair<int,int> > v;

A:

I think you might have accepted that answer a little too quickly.  The commonly accepted way to do this is like this:
vec.emplace_back (x, y);

And if you look at Godbolt, you can see that this inlines everything (which may or may not be what you want):
https://godbolt.org/z/aCl02d
Run it at Wandbox:
https://wandbox.org/permlink/uo3OqlS2X4s5YpB6
Code:
#include <vector>
#include <iostream>

int x = 1;
int y = 2;
std::vector<std::pair<int,int>> vec;

int main () {
    vec.push_back(std::make_pair(x, y));
    std::cout << "make_pair done\n";
    vec.push_back({x, y});
    std::cout << "push_back done\n";
    vec.emplace_back (x, y);
    std::cout << "emplace_back done\n";

    for (std::pair <int, int> p : vec)
    {
        std::cout << p.first << ", " << p.second << "\n";
    }
}

Output:
make_pair done
push_back done
emplace_back done
1, 2
1, 2
1, 2

Of course, everything runs faster if you reserve the appropriate number of elements in the vector up front.  Maybe that's what the people posing this question are really wanting you to say.

A:

I tried this in an online compiler, and as far as I can see the optimized assembly for make_pair is identical to {} syntax.
https://godbolt.org/z/P7Ugkt

A:

{x, y} in v.push_back({x, y}) is aggregate initialization (since C++11) of v's value_type, whereas std::make_pair is a function creating and std::pair with types deduced from its arguments.
One advantage of push_back({x, y}) over emplace_back(x, y) is that you could keep small structures simple (without constructors) like this:
#include <vector>

struct A {
    int x;
    int y;
    // A(int _x, int _y) : x{_x}, y{_y} {}
};

int f()
{
    std::vector<A> v;
    v.push_back({1, 2});
    // v.emplace_back(1, 2); // doesn't compile unless constructor is uncommented
}

Example.

