Can I use any kind 20W50 motor oil in my motorcycle, even if its not specified as motorcycle oil?

I purchased several bottles of Castrol 20W50 High Mileage Synthetic oil for my motorcycle, and then the next day I saw the section for just motorcycle oils, and was wondering if it really mattered. The manual says to use 20w50 oil w/ detergent, and this Castrol high Mileage stuff meets the criteria, but I guess technically it is a automobile lubricant. Do you think it would cause problems in my bike? It's a 2000 Ural Tourist, 4 stroke, 2 cylinder 650cc and the same oil is used in both the main chassis and gear box.