I'm kinda confused about stand_and_carry_position.

In one point on the wiki, it says that typically characters should face each other, and if they face away from each other the tag should be reverse_stand_and_carry_position.

But the example image shows what I think would be reverse_stand_and_carry_position. And there's no implication involved between these tags.

Examining the tag, looks like people are tagging both cases as stand_and_carry_position. I find this kinda redundant and unnecessary if these are separate tags.

I wanted to start fixing this tag, but I wanted to make sure first: did I understood the definition of the tag right?

Judging by the wiki's edit history, it seems like the thumbnails were a leftover from the first iterations of the wiki (i.e., there was no distinction between facing each other or away from one another).
It was only through the addition of reverse_stand_and_carry_position that the wiki's thumbnails became inaccurate.

In that case, you can change the tags of the relevant posts to reflect these changes. Even find new example thumbnails for the stand_and_carry_position wiki and its counterpart.

Just warning that I updated the description based on this.

It is good now. I think stand and carry is the main position that is known everywhere. The reverse version is just a e621 thing that makes a distinction between the facing of the carried partner. In more common use, such precision is not necessary. We hadn't before had the courage to remove the option for stand_and_carry applying for both. Good that you did it now.