FBI Mnemonics And Right Hand Rule Do Not Work Together?

Apprently ive forgotten lots from school and was just messing around today.

Everyone knows through lenzs law and the right hand rule that a current going through a wire will produce a field according to the right hand rule

I discovered today or remembered more likely that the FBI Mnemonics for a motor apparently violate this.

Can someone confirm this?

If you were to draw a simple loop with two poles north and south the two laws violate each other. I thought the right hand rule always held true for current through a wire.

Apparently im loosing my mind

To use the left hand rule for motors you must have to know more then just the direction of current because you could hold your left hand more then one way.

What am i missing here.