Boiled potatoes are very interesting. They contain a lot of starch, but when a boiled potato cools down (i.e. on your plate) then the starch in the potato turns into something called 'resistance starch'.

Resistance starch stays intact more until the intestines where it acts as a fibre for intestinal flora. Cooled rice also has this affect too. I think this sense of the starch keeping form for longer is what's ultimately responsible for the difference. Fibre and starch and proteins keep their forms longer which contribute to a feeling of fullness. Focusing on calories alone doesn't work for example, you can consume a lot of calories in sugary alcohol and not feel full compared to the same calories in food. This is because the drink is more fluid (less fullness) and the calories are absorbed significantly quicker and earlier in the digestive tract.

As others have pointed out, water content, portioning size (small individual chips vs bigger potatoes) also come into it.