After Britain lost American colonies they gained a few new colonies in other areas. In 1713 Great Britain acquired the French colony of Arcadia and soon after the colony of Canada. Also in 1763 Britain acquired the Spanish colony of Florida but the main place where they were able to gain new colonies was in Australia. So although they lost some colonies in America they were still able to acquire others elsewhere like in Australia.
They differ because they are 2 different constitutions.
The Declaration of Independence states that the authority to govern belongs to the people, rather than to kings, that all people are created equal and have rights to life, liberty and the pursuit of happiness. The American colonies had been at war with Great Britain for over a year when the document was signed.
The answer is the Kansas-Nebraska Act