So far, they haven't gone into how sensor ninja skills work but we know for sure sage mode has a visual aspect to the sensing, a mental projection you can call it.
What we can tell from sensor ninjas, once they sense a certain chakra they then memories that feeling(dark,bright, chakra amount, chakra flow etc..) and associate it to that person when they actually SEE THE PERSON after they sensed it. That's how they can identify targets with chakra, sense a chakra then see that person and memorize that correlation. For example Karin couldn't tell Naruto was surrounding her, sasuke, jugo and Suigetsu with hundreds of clones only that there are a lot of the same chakra everywhere(this was during the itachi hunt arc). But she could locate Danzo without seeing him as she saw him enter the kage meeting before the meeting started.
But sage mode on the other hand is able to visualize what the user is sensing and able to associate that to a person without needing to see the targets before. For example when Naruto returned to fight Nagato, he knew didn't sense Kahashi's chakra in the village even though he's never sensed his chakra before but he knew he wasn't there, same with Hinata as well. So sage mode in a way is like a crystal ball looking at a area and mentally seeing whats present in the area. That's the only way for Naruto to actually know Kakashi's chakra wasn't in the village at the time among all the other villages, Naruto was mentally searching for kakashi and we all know found no signs of his chakra. Look at the pictures of Naruto tracking down Nagato again, hes actually seeing within his mind where the chakra is going. Quite incredible if you think about.