Difference between Betray and Backstab
Solution 1:
Your example:
A trusts B with his bank account, but B steals from A
...is both a betrayal and a "backstabbing."
A backstabbing is a specific kind of betrayal; it is a secret or covert betrayal. It is to betray someone "behind their back," thus "stabbing them in the back."
In romance, think of the distinction between "dumping" a partner (leaving them) and "cheating on" a partner. If a person says "I don't love you anymore, I'm leaving you" their ex-lover may feel betrayed but has not been backstabbed unless there was some secret before the breakup.
All backstabbings are betrayals, but they may be very small betrayals. A distant acquaintance or a coworker may not owe you any loyalty. That person can't "betray" you outright, but they can still "stab you in the back" by simply pretending to be friendly "to your face" while working secretly "behind your back" to hurt you.