Limes and lemons are both citrus fruits that are rich in Vitamin C, but yes they are different. For one, lemons are yellow while limes are green. Limes are also smaller than lemons.
As for the health benefits, lemons are known to prevent vomiting, throat trouble, acidity and rheumatism. It is also a powerful antibacterial, and can destroy intestinal worms.
Limes, on the other hand, aid respiratory disorders and is higher in Vitamin C, A, calcium, iron, and phosphorus