运动means do exercise,体育always means physical education,especially in school,we have a class called 体育.
照片 means photo，picture,noun,照相 means take a picture ,verb
办法 means method,ex:我有办法（means i have a idea,i know how todo something,it's concrete)
方式 means mode\manner\style,ex:做人的方式（means how to be a man,it's abstract)
方法 means approach，ex:学习方法（means a way to learn，well,sometimes 方式和方法也可以互换)
ex:你的方式\方法不对（the way you did is wrong)，这是个好办法(this is a good idea or method)
If you still have any questions,youcan ask me :)