Lure, bait, decoy, snare, trap all denote something that leads an animal or a person into a particular place or situation from which escape is difficult.
Lure suggests something that always attracts and often deceives yet does not necessarily lead one into evil or into danger. Often the connotation of deception is subordinated or lost and that of drawing power or seductiveness is correspondingly heightened.
Bait basically applies to a morsel of food by which a fish or other animal is enticed into a situation where it can be caught. In extended use it is applied to something, often in itself relatively insignificant, which is held out as a temptation or as a suggestion of an inviting prospect in the hope or with the result of inveigling someone into a desired act, position, or situation.
Decoy may apply to a wildfowl or the likeness of one which is used to lure other wildfowl into shooting range or into a net. In extended use it is applied to a person or sometimes to a thing that leads one to go somewhere or to do something that exposes one to the danger of being entrapped (as in the commission of crime, in compromising or unpleasant circumstances, or into being used to further another person's ends).
Snare basically applies to a line with a running noose for catching a bird or animal. In extended use it is applicable to a danger one may run into accidentally or unexpectedly or through lack of caution or wariness and from which, once involved, one cannot easily extricate oneself.
Trap basically applies to a device that shuts with a spring for capturing animals. In extended use it is, like snare, applied to what is a danger to the unwary or incautious. The two words are often used interchangeably as though they were indistinguishable in meaning; however, trap is preferred to snare when disastrous effects, or deliberate setting for the purposes of capture, or trickery beyond detection are implied.