The plot of each story is quite different: in "The Lottery," a town is selecting the next person chosen to be stoned to death. It is a long-standing ritual, and there is a sense that it serves to get out the aggressions of the townspeople, and has even be suggested that it has been used to cut down on violent crime. In "The Lottery," the woman chosen (Tessie Hutchinson) argues about her selection, believes it is unfair, and, of course, does NOT want to participate, but has no choice.
In "The End of the Party," a young boy (Francis) has a terrible fear of the dark. He has been invited to a child's party where he knows there will be a game of hide-and-seek played, and he is frantic for fear of having to participate. He is forced to go, does participate in the game and, it would seem, dies from fear in the dark while hiding.
In both stories, the main characters are forced to do something against their will. While one story has a very dark premise (a lottery to select a victim), the other would seem to promise a positive story as the word "party" is used, but in both cases, the title is misleading at first glance.
Both characters are unwilling participants, in both cases, each is forced to participate, and at the end of each story, our character dies. Though the cause of death on a death certificate would read differently for both characters, each dies as a result of their inability to avoid being forced to take part in an activity each desperately wants to avoid.
An obvious difference between the characters is that one is an adult, and one is a child, but the similarity between both is that each, regardless of age, is forced by the adults around him/her to be a part of something neither wants to be involved in. In both cases, the character dies because of this inability to act upon his/her free will.