There really is no fine line in between the two. They tend to overlap and so we become unsure of what is right and wrong. Yes, George did kill Lennie but he didn't murder him. The words kill and murder may seem to mean the same thing but in reality they don't. George gave to Lennie what any true best friend would do in their situation, a mercy killing. George and Lennie were like family towards each other and George killed Lennie himself so he wouldn't have to go through the torture by Curley.
George and Lennie were best friends ever since they were little. Even after they grew up they still stayed friends and George was always there to protect Lennie. Sure, George may have been mean to him but it was for the best in the long run. He always looked out for him and helped him go though life. They were like family towards each other and loved each other till the end. There dreams was what kept them going. In fact, their dreams always included Lennie feeding the rabbits. Without him, .
At the end George did what was the only right thing, a mercy killing. If George hadn't killed Lennie then Curley would have tortured. But why would Curley want to kill Lennie in the first place? Because Lennie accidentally killed Curley's wife. Yes, it was an accident and should be forgiven but Curley wasn't going to let this slid. No, Curley wanted revenge. So George had no choice but to end his best friend's life. But not only that, George even made Lennie think about his dream and happy thoughts during his last minute. George told Lennie that he was never mad at him and started talking about their dream with the rabbits. Lennie love rabbits and his last thoughts were about the rabbits.
George didn't murder Lennie. He gave him a mercy killing, rather than Curley's torture. George loved Lennie with all his heart and never wanted to live a second without his friend. George didn't do anything wrong, he just did what he thought was best.