Approach from which side
This dilemma is mainly about the 4-4 and 3-3 points (which are symmetric in the corner). There are examples for the 4-4 point at joseki repertoire for mid-kyu players
The 'usual' approach moves to the 3-4, 3-5 and 4-5 points are on a given side. One exception from recent times has been in the Chinese fuseki.
The normal approaches to 3-4 are at the points a, b, c and d. A play such as White e can be answered by enclosing the corner at a or b, which puts Black ahead on territory locally.
In the particular case of the Chinese formation adopted by Black, here has become accepted. If now Black a, White b gives a playable overall position. Therefore at b has become a pro variation.
See 3-4 point approach from the wrong direction for more on this.