in the end, finally, after all, at last, finally, ultimately
at the end, end; end, extreme limit
at an end, end, end, finished
in the end is more abstract, one thing, the end of a period.
Oxford Example: In the end, they decided to spend the holiday at
homeOxford Example: He tried many different jobs; in the end he became a postman.
at the end is more specific, the end of the place, the end of time, the end of the movie
eg : the house at the end of the street, at the end of the day, month, year
Oxford Example: Turn into Hope Street and our house is right at the end
at an end, used with the verb be
Oxford Example: The war was at an end. The war was over.