Almost certainly the same unit. The Mysore Lancers were an Imperial Service Unit - a regiment raised by one of the princely states, Mysore in this case, who were attached to the British Indian Army, mostly during WW!, though a few IS units did take part in some of the colonial campâigns of the 19th century as well, if memory serves.
Now best remembered for the charge at Haifa in Palestine in 1917, one of the last and more successful cavalry charges of that war. The Mysores were absorbed into the 61st Cavalry, Indian Army, after Independence - the last horsed cavalry unit in India, though it is apparently about to lose its mounts.