I'd say Gordon absolutely DOES know it's a different Batman, but it's important to him, his men, whoever it is in the Batsuit and at a deeper level, to the city itself, that he acts as if this were the same Batman he's always dealt with. And he probably sense's that it's the guy he used to know as Robin and Nightwing, but he's keeping that to himself.
Robin's are more variable, he's met multiples of them and knows they come and go, even if he did assume Tim was Jason in a new costume the first time they met.