One and the other; relating to or being two in conjunction: Both guests have arrived. Both the books are torn. Both her fingers are broken.
The one and the other: Both were candidates. We are both candidates. Both of us are candidates.
Used with and to indicate that each of two things in a coordinated phrase or clause is included: both men and women; an attorney well regarded for both intelligence and honesty.
American Heritage(R) Dictionary of the English Language, Fifth Edition. Copyright (c) 2011 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.