One way to tell is to examine the shoe up close: If you can see the pores in the leather, it is likely full grain. If the leather looks very smooth, and a bit plasticky, then it is probably corrected grain. The sanding process used in corrected grain finishes will cover up the pores.
If the leather is truly genuine and minimally processed, one thing you will notice is the imperfection -- scratches and cuts on the hide of the animal will still be there, and the two shoes in a pair will have different blemishes. This is actually something many aficionados find desirable -- a kind of uniqueness, if you will. I have some pairs of shoes that are like this, notable among them a pair of Grenson slipons made in England, and they look great to me, blemishes and all.
I looked at the model you mentioned on the J&M website, and it is hard to tell from the picture, even with magnification.
By the way I own vintage models of Aristocraft and Crown Aristocraft shoes, and those are all full grain leather. They are also beautifully made, welted shoes with proper stacked heels -- constructed the old-fashioned way!