What are the differences between 锻炼 and 运动 for "exercise", "work out", "train", etc?
运动 means "to exercise" or "to work out" . It is basically a method of strengthening one's muscles through body movements, to gain power and  or improve endurance in sport.  It can also just for keeping one's body healthy and fit. 

锻炼 means "to train" or "to practice" . It refers to "improve skill and ability through training and practicing" It can apply to any thing that require skill and physical ability. For example, you can 锻炼 your language skill, chess playing skill or  your eye sight.  运动 is one of a methods for someone to 锻炼 his physical ability. 


运动 as a verb can be used without object. e.g. "you need to exercise more" (你需要多运动)
锻炼 as a verb usually be used with object. e.g. "you need to train your hand eye coordination more (你需要多锻炼你的手眼协调)