Everyone with Bitachon is a believer, but not every believer has Bitachon.
The Ramban explains that in order to have Bitachon you must believe in Hashem, otherwise who would you be having faith in? But believing in Hashem does not mean that you have Bitachon. There’s often a doubt in our minds whether we will receive help from Hashem because maybe we’re not worthy of it. We feel like we do to many aveiros. We even find that Ya’akov Avinu was worried that he would be harmed by Eisav because he may have sinned.
But the truth is as the passuk says, “בטח על ה’ ועשה טוב” – First trust in Hashem, then do good. Chazal even say that even a rasha who has Bitachon is surrounded with chesed of Hashem. (The Gr”a even goes as far as to say that a thief who has Bitachon that he will be successful in stealing will be successful).
This doesn’t mean that sins will be overlooked. Rather, they are not considered when Hashem helps a person who trusts in Him.
So why then was Ya’akov afraid that his sins would affect him?
When we look at what Ya’akov Avinu did, we notice something interesting. He split up his camp into two groups so that if one was attacked the other could still survive. But intstead of splitting his family into two, his entire family was in one group and only his servants and flocks were in the other.
Ya’akov had complete Bitachon that nothing would happen to him or his family. It was only with his possessions that he was worried that his sins would cause harm to him.
Every person can have Bitachon and every person will be helped when they have Bitachon.