Abram and Abraham are the same person. Abraham was named Abram when he was born and he was called Abram until he was 99 years old, when God changed his name to Abraham. In that day it was not uncommon for your birth name to be changed. It usually indicated an important change in your life.
Ab means Abba or father, and ram means high. So Abram means high father. Abraham means a father of a great multitude.* God promised Abraham that He would make him a father of many nations (Gen 17:5-8).

Abraham lived in Ur with his father, Terah; his nephew, Lot; and his wife, Sarah. Ur was a booming community on the Euphrates River. The people who lived there believed in many gods but Abram believed in only one God. Terah moved the family to Haran. After Terah died, God spoke to Abram and asked him to move to the land of Canaan. Abram was obedient and immediately set out for Canaan. He went to Shechem and to Beth-el (both cities in Canaan), then to Egypt (during the famine), back to Beth-el, then to the grassy lands of the Negeb in the south, back to Beth-el, and finally to Hebron. He was led by God to move from place to place throughout his life.

* Jamieson, Robert, A.R. Fausett and David Brown. A Commentary. Grand Rapids: Eerdmans Publishing Co. 1993. p. 151