Marshmallow (Althea officinalis) shares the same mucilaginous properties as the malvas that are also known as mallows. Either will work, but what you will find in health food stores will the marshmallow. Malvas are common weeds though, which is why I mentioned common mallow. It is something easily identified and collected if it grows near you giving you another option if you cannot get to a health food store right away or cannot find marshmallow root.
The most common malva you will find growing as a weed will be common mallow (Malva parviflora). The leaves are used with this plant though instead of the root as with marshmallow.