So a positive belief is like faith that something will occur, very often betraying the factors that influence the outcome. "If all I do is believe that I will achieve it, then the universe will reward my belief." This can be dangerous because it can twist reality to coerce an individual into compromising scenarios.
A useful belief is like a set up, to encourage or discourage behaviour, very often with awareness of the underlying factors that influence the outcome. "If I believe that my skills are improving, then I feel more compelled to invest in developing those skills."
The distinction has come about because too many people have strayed away from the reality that positive belief encourages behaviour rather than influences an event. Useful belief retains that the belief has a purpose to encourage behaviour that influences an event.
Think of all those charismatic and exploitative gurus out there who sell good feelings for hard earned cash. Positive belief is often at the core to compromise a persons logic to swindle trusting people.
Thanks for the explanation and examples. The use of positive beliefs seems to give a emotional boost for the short term but does not promote long term change in behaviors and habits. Using useful beliefs may help someone persevere the challenges ahead towards long term change more so than positive beliefs.