excellent thread, these terms are often used without understanding the true meaning. For example, there are some who don't believe in God. This would be unacceptable to many including me.
What is more important in my view is that the context in which it's used, the circumstances in which a human being finds himself or herself and lastly the commercialization or exploitation by some individuals.
For instance, when we hear a loved one who's fallen sick or who's met with an accident we pray to "God please let him be safe". Many parents keep images of God in the kid's bedroom when they start sleeping in their own bedroom. These are beliefs and there are much more examples that rational people still follow.
When a family goes through difficult times or the earning member loses his job or glass breaks during an auspicious day at home, many well-educated people get disturbed and depend on the extent of the impact of the event they start going to places of workship, donate food to poor or do pujas to ward of ill-luck. To me, these necessarily do not mean that we are irrational. We live in a world of constant change and stressful periods of home and career. When a minor mishap or a calamity sadly falls on a family, then it tests them to the fullest. It is at these difficult times that we need to believe in a higher power, believe the worst will pass. To me, belief leads to hope and hope is important for life. People who are have gone through such phases in life would agree with me.
Last but not the least, these human thoughts should not lead to or foster greed, inhuman acts, unsocial acts or follow so-called Godly men and women who exist only to extract money and favours out of the unfortunate fellow human who is already going through a difficult time.