"Believer" actually means "one who acknowledges God". God describes them as those who Respond to Him. Its less about "belief" and more about the "doing".
"The Righteous" actually means "God Conscious". God describes them as those who responded and who Worship God Alone, not simply "believe" in God Alone. They consistently observe the Contact Prayers daily and they give the obligatory Charity. They are "appreciative" so they obey God they uphold His Commandments. They believe in God's Revelations and are called the repenters and the doers of good works. They believe they are held accountable to a higher authority than themselves and they avoid sins and they are advocates for good. They give sincere effort to improve themselves before God and they follow God's Path and practice all aspects of the Religion He has decreed. (This is not a complete list of traits of the righteous, but it makes the point.)
"Leading a Righteous Life", is described as simply doing the "righteous works" listed above and many others. It is also developing our Souls by actively practicing the Religion as decreed by God in our lives.
"Disbeliever" is naturally the opposite of the "Believers". They are the idol worshippers and atheists. They are also described as those who do not respond to God, or do not worship God in the manner He decreed, or do not obey Him, or do not believe in His Revelations, or do not uphold His Commandments or do not follow God's Path or practice the Religion He has decreed. This description includes people who say "I believe" yet fail to become "Righteous" and fail to follow His Path or practice their religion seriously. That's a huge point to understand; that many people who say they "believe" are classified by God as "disbelievers" because of what they do and do not do.
God just defines and describes these terms and categories of people but it is our choices and behavior in our lives that put ourselves into any of them. Its the Test of this life and we will invariably choose where we will end up.
The thing we have to remember is that how we judge ourselves, in relation to the world, is one thing. The way we judge others and how we judge our friends and families according to our "worldly" standards is one thing. We can easily confuse our relationship with the world with our relationship with God and the sad truth is that the world may love us, but God may not. God judges all of us by our relationship with Him, not our friends, family or society. It's how we treat that relationship with Him, that is really going to matter to us on Judgement Day.
