Are a Lambda probe and an exhaust temperature sensor the same thing?

They are two different sensors, even if both are fitted to the muffler. In fact, an exhaust temperature sensor detects the maximum and minimum temperature of exhaust fumes: an important piece of information when checking whether carburetion is correct. It is fitted inside the exhaust pipe at a distance of about 15 cm from the exhaust port.
Compared to this sensor, a Lambda probe gives a more precise assessment of the actual state of carburetion, as it measures the amount of fuel and unburnt oil that remains inside the muffler, allowing us to understand the real "stoichiometric ratio". As mentioned, a Lambda probe is also fitted to a kart’s muffler, but unlike an exhaust fumes thermocouple sensor, it does not have to be at a set distance. Both sensors can be used simultaneously to better assess the correct carburetion of an engine.

In my opinion, this assertion is completely false. A real difference, in terms of lap times, can be had by improving acceleration on exiting bends. As a result, if you can improve engine performance at low revs, you gain time on every bend; vice versa, if you improve it at high revs, you can only take advantage on the straights, of which there are usually quite few compared to the mixed sections on kart tracks. Ultimately, in general I would advise using a muffler that helps the engine at low revs: that usually results in faster lap times.