pencil box/pencil case/pencil pouch

Which would Americans call these, a penncil box, a pencil case or a pencil pouch?
1. https://forum.wordreference.com/prox...598e09913a6a8a

2. https://forum.wordreference.com/prox...b379d51ad8c02f

3. https://forum.wordreference.com/prox...5728f1a8516ed6

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I think
"pencil box" have rigid sides
"pouch" in this case is a small bag
, and I think we can call "a pencil box" or "a pencil pouch" a pencil case.

So #1 is a pencil pouch or a pencil case.
#2 is a pencil pouch or a pencil case.
#3 is a pencil box or a pencil case.
I wanted to check whether I'm right.
Thanks in advance!http://forums.photographyreview.com/...ABAAEAAAIBRAA7

Yes, you do have a really creative ideas and good pouches for pencil but I recently discovered a great website from where you can get cute pencil cases, zippered pencil cases, cute pencil cases, razor backpack, and more at too reasonable price also their quality awesome that I got it.