To be honest, this is the first time I have come across oral "cleanser" as normally I'd associate a cleanser with the skin. When Googling this there is really only one product that comes to the fore as an ORAL "cleanser"

But yes, you're right as there seems to be a difference between "cleanser and "mouthwash" https://www.wegmans.com/products/personal-care-and-makeup/or...

There seems to be a difference in how they are USED. Note that the cleanser is

"For minor mouth or gum irritations. Cleanses dental appliance irritations. Soothes canker sores. Kills odor-forming germs..." BUT look at the warning

"Warnings: Do not use: this product for more than 7 days unless directed by a dentist or doctor. "

So that is for using it straight from the bottle where you are only using a few DROPS.

https://www.drugs.com/drp/gly-oxide-liquid.html

Directions For Temporary Use: Do not dilute. Replace tip on bottle when not in use. Adults and children 2 years of age and older: Apply several drops directly from bottle onto affected area; spit out after 2 to 3 minutes. Use up to four times daily after meals and at bedtime or as directed by dentist or doctor. OR place 10 drops on tongue, mix with saliva, swish for several minutes, and then spit out. Use by children under 12 years of age should be supervised. Children under 2 years of age: Consult a dentist or doctor.

Directions For Everyday Use: The product may be used following the temporary use directions above. OR apply Gly-Oxide to the toothbrush (it will sink into the brush), cover with toothpaste, brush normally, and spit out.


So, unlike a mouthwash which you swill around the mouth in whatever quantiy directly from the bottle before spitting out, here you are using only a few DROPS of the liquid and then letting your own saliva act as the main liquid. You are also dabbing these drops directly against the infected area.
So, in general it seems it is much easier if this cleanser is just for short-term use, (7 days) to clear up irritations which may be caused by dentures and then to use mouthwash on a daily basis.

Mouthwash is intended to be used every day and is what most people are familiar with. Most toothpaste manufactureres make mouthwash as well and many dentists recommend that people use them after brushing and flossing as a way of rinsing the mouth
https://www.ada.org/en/member-center/oral-health-topics/mout...