First: the two different ways are really "overload as a member" and "overload as a non-member", and the latter has two different ways to write it (as-friend-inside class definition and outside class definition). Calling them "inside class" and "outside class" is going to confuse you.
Overloads for +=, +, -=, -, etc. have a special pattern:
struct Vector2 {
float x, y;
Vector2& operator+=(Vector2 const& other) {
x += other.x;
y += other.y;
return *this;
}
Vector2& operator-=(Vector2 const& other) {
x -= other.x;
y -= other.y;
return *this;
}
};
Vector2 operator+(Vector2 a, Vector2 const& b) {
// note 'a' is passed by value and thus copied
a += b;
return a;
}
Vector2 operator-(Vector2 a, Vector2 const& b) { return a -= b; } // compact
This pattern allows the conversions mentioned in the other answers for the LHS argument while simplifying the implementation considerably. (Either member or non-member allows conversions for the RHS when it's passed either as a const&
or by value, as it should be.) Of course, this only applies when you do actually want to overload both += and +, -= and -, etc., but that is still common.
Additionally, you sometimes want to declare your non-member op+, etc. as friends within the class definition using the Barton-Nackman trick, because due to quirks of templates and overloading, it may not be found otherwise.