丢 (diū) is the everyday, colloquial word for both 'to lose/misplace' and 'to throw away/discard'. For losing something, it's more common in speech than the formal 失去 (shīqù) or 丢失 (diūshī). For discarding, it's similar to 扔 (rēng), but 丢 is more about getting rid of something while 扔 can also mean physically throwing an object.