Twist has multiple meanings, as both a verb and a noun. As a verb, it means to contort or wrap in a spiral pattern, and also to distort or change the meaning of words or ideas.
Ex: Trying to tie two ropes together, all I ended up accomplishing was twisting one of them around the other about fifteen times. Finally, they got so tangled that they stayed where they were.
Ex: My father had told me to be home before eleven. When I got home at one a.m., I told him that he hadn't said 11 p.m., so I hadn't really broken the rule. He got so angry at me twisting his words that way that he couldn't speak.
As a noun, twist can be an unexpected turn of events in a story, as well as a sliver of lemon peel that has been twisted, usually served as a garnish in a cocktail.
Ex: I love the short stories of Roald Dahl, because they are usually full of irony and always end with a twist that makes you laugh, or think, or both.
Ex: I always make a point of asking for my martinis with a twist instead of an olive, since the lemon makes the already cold drink seem even colder.
Like twist, bend has many meanings. One meaning as a verb is cause something to change shape, from straight to curved. Another is turn or change direction. In this sense, bend can also be used as a noun, referring to the place where a road curves.
Ex: Tom held the straight aluminum bar in his hands, and slowly began to apply pressure, eventually bending it into a curved ninety degree angle.
Ex: We could see, looking at the map, that the road continued going on straight, following the ridge for some time, before bending to the south to go around the reservoir.
Two expressions that use bend are bend over backwards, which means working very hard to help someone, and bend the rules, meaning change the rules or allowing someone to break them.
Ex: I don't know why he wouldn't call to thank me. I helped him with his CV, put in a good word for him with the HR department, and helped him get the salary he wanted. I practically bent over backwards for him.
Ex: Mr. Goodman told me that while I should really be disqualified, he might be willing to bend the rules of the contest and allow me to compete because I "had the right spirit”.