Ok, so, I lied. The cleanser wasn't rice or oat or even from the same brand the snail mulch mask was from. It's a green tea cleanser from a brand called Missha and I paid around $8.49 CAD for this. Unlike MJCare (the brand who makes the snail mulch face mask) I was actually able to find the brand's website and I learned that they have two other cleansers in this line; strawberry one for moisturizing and radiance and a coca one for dryer skin types. (https://missha.ca/collections/skin-care-1/products/missha-creamy-latte-cleansing-foam-172ml).
This cleanser is very thick and has a delicate, almost creaming foam to it. 
This cleanser is aimed toward oily skin so I do find it a bit drying on my cheeks since I have combo skin, but not overly so. When I use this my skin feels very clean but not stripped? It's hard to describe I've never experienced anything like that before. I do like using though and I get no irritation from it so I'm not too worried.
:0 Which ones?
I'm in shock that I found such a hidden gem at a convenience store of all places I hope they keep on restocking it.
The Ultra Hyalron Ampoule 10X, and Essence 10x. I feel like my skin has gotten a lot of spring back because of these two, but I also have very sensitive skin and theirs are one of a few hyaluronic acid lines that don't break me out. I tried the peeling gel too, but I like the e.l.f one better.
I hope they keep restocking it for you too :) Maybe they will expand the offering if you express interest? I'm going to have to try one of the cleansers you linked!