The pose called "Forward Virasana"

I have been moving in yoga circles for some time now with people who call the pose you see above "forward virasana". In fact I just now did a little search in Google images for forward virasana and found lots that looked a lot like this. Sometimes the knees are a little part, like this, sometimes together. Call that variations for individuals.

I have a problem with the name.

The picture below is virasana.

I think this fellow is sitting on a block, a sensible variation for many of us, but in virasana, hero's pose, the bottom is between the feet, not on them.

Below is vajrasana, thunderbolt pose:

 Notice that in Vajrasana the bottom is on the feet.

So why, when from a kneeling position the body is draped forwards with the bottom ON the feet and arms reach forward, do we call it forward virasana?

I will even go further and ask, why forward?  It appears to me to be more folded, or downward facing.

So might the pose be more properly called "adho mukha vajrasana"?

I have another suggestion: "Dwiputasana: or "double fold pose". 

Also what is the difference between this "dwiputasana" and "utthitha balasana", extended child's pose?

To me it is the engagement or lack of it.

Below is balasana and its utthita (extended) version, The extended version has relaxed arms, forearms resting on the floor. Following that is our "dwiputasana" again, and notice that the arms are active. The head may not even be on the floor but may be actively reaching towards the hands.

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So, do you think we should change what we say when we take this pose? If so, what will you call it?