Number of Solutions for Brute Force Algorithm of Travelling Salesperson Problem
In the classic variant of the Travelling Salesperson Problem, the distance from X to Y is the same as the distance from Y to X for any two locations X and Y. Hence, as you noticed, an algorithm does not need to distinguish between the two solutions A, B, C, D and A, D, C, B. However, whether a brute force algorithm considers both solutions or not would depend on how exactly it is implemented. Some will and some won't. It is not too much of a waste to consider them both -- after all, it only takes twice the time. And it may be easier to program the algorithm that way. 

There is also a so-called asymmetric variant of the Travelling Salesperson Problem where the cost of moving from X to Y is not necessarily the same as the cost of moving from Y to X. Note that in this case, the two solutions A, B, C, D and A, D, C, B are not "essentially the same" anymore and it is important to consider them both.