I read your answer about Ice skating on shabbat - while ice skating the blades cause a ridge in the ice. I read once that one is not allowed to pull a chair (or bed i’m not sure) on the ground on shabbat if it causes a ridge. What is the diffrence between this two ridges that you are not allowed to pull a bed but you are allowed to ice skate and cut the ice with the blade on shabbat?

Pulling a heavy chair or bed makes a noticible ridge in the ground, which is similar to "plowing" in the sense that the ridge could be used to plant small seeds. This is not the case with the minute ridge in the ice. It would in fact be forbidden to skate in a way which could be conceived as drawing pictures or designs on the ice, even if temporary, but I believe this is not the normal case.