according to the website of Sigma (a provider) and in the FAQ section, you can read that;
'The type designation does not have any particular biological significance. It is used to emphasize differences in the listings of this product'.
It is also mentioned that;
Product No. M2378 (Type II) is a crude mucin preparation. Product No. M1778 (type III) is a partially purified powder prepared according to the method described in Glenister, D.A. and Salmon. K. Microbial Ecol. in Health & Disease 1, 31, (1988). The amount of bound sialic acids are also different'
I have the same issue. The differences are quite hard to ascertain. From my studies, the first difference is the price. HGM III costing approximately 4 times more than HGM II. Although both are far less expensive than mucin from bovine submandibular glands, discontinued by many suppliers. The Sigma website states that type II contains 1% sialic acid where tye III contains between 0.5 and 1.5%. Doesn't appear to be much difference there. Another difference is that type III is partially purified, and this likely justifies the cost difference. Finally, there is a preparation note associated with type III stating "Prepared according to the method of Glenister, et al., for use in complex growth media for dental plaque bacteria." (Glenister, et al.1988). I have used HGM III in an artificial saliva medium for just this thing.
From Glenister et al.
Alternatively, plaque bacteria were cultured in the defined saliva medium of Shellis (1978), except that the principal glycoprotein, bovine submandibular mucin, was replaced with hog gastric mucin since this is not only cheaper but also is much more closely related to the human material than the bovine mucin (Herp et al. 1978).